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mathematics
precalculus

Questions and Answers of Precalculus

(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. Find b so that the vectors v = i + j and w = i + bj are
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. Find a so that the vectors v = i - aj and w = 2i + 3j are
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i, w = -3j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 4i, w = j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 3i - 4j, w = 9i - 12j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 3i + 4j, w = -6i - 8j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i + √3j, w = i - j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = √3i - j, w = i + j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 2i + 2j, w = i + 2j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 2i + j, w = i - 2j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i + j, w = -i + j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i - j, w = i + j
True or False. Work is a physical example of a vector.
True or False.Given two nonzero vectors v and w, it is always possible to decompose v into two vectors, one parallel to w and the other perpendicular to w.
If v = 3w, then the two vectors v and w are ________.
If v.w = 0 then the two vectors v and w are ________.
If v = a1i + b1j and w = a2i + b2j are two vectors, the _____ is defined as v.w = a1a2 + b1b2.
In a triangle with sides a, b, c and angles A,B,C the Law of Cosines states that _______.
Show on the following graph the force needed for the object at P to be in static equilibrium. (a) Draw v and then use the red vector to show 3v.(b) Use the red vector to show -v.(c) Draw v and
A farmer wishes to remove a stump from a field by pulling it out with his tractor. Having removed many stumps before, he estimates that he will need 6 tons (12,000 pounds) of force to remove the
At a county fair truck pull, two pickup trucks are attached to the back end of a monster truck as illustrated in the figure. One of the pickups pulls with a force of 2000 pounds and the other pulls
Repeat Problem 87 if the angle on the left is 3.8° the angle on the right is 2.6°and the weight of the tightrope walker is 135 pounds.
A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 150 pounds, how much tension is in each part of the rope?
A weight of 800 pounds is suspended from two cables, as shown in the figure. What are the tensions in the two cables? 50° 35° 800 pounds
A weight of 1000 pounds is suspended from two cables as shown in the figure. What are the tensions in the two cables? 25° 40° 1000 pounds
The pilot of an aircraft wishes to head directly east, but is faced with a wind speed of 40 mi/hr from the northwest. If the pilot maintains an airspeed of 250 mi/hr, what compass heading should be
A river has a constant current of 3 km/hr. At what angle to a boat dock should a motorboat capable of maintaining a constant speed of 20 km/hr be headed in order to reach a point directly opposite
A magnitude of 1200 pounds of force is required to prevent a car from rolling down a hill whose incline is 15° to the horizontal.What is the weight of the car?
A magnitude of 700 pounds of force is required to hold a boat and its trailer in place on a ramp whose incline is 10° to the horizontal. What is the combined weight of the boat and its trailer?
An airplane has an airspeed of 600 km/hr bearing S30°E. The wind velocity is 40 km/hr in the direction S45°E. Find the resultant vector representing the path of the plane relative to the ground.
An airplane has an airspeed of 500 kilometers per hour (km/hr) bearing N45°E. The wind velocity is 60 km/hr in the direction N30°W. Find the resultant vector representing the path of the plane
Airbus A320 jet maintains a constant airspeed of 500 mi/hr headed due west. The jet stream is 100 mi/hr in the southeasterly direction. (a) Express the velocity va of the A320 relative to the
A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north.The jet stream is 100 mi/hr in the northeasterly direction. (a) Express the velocity va of the
Two forces of magnitude 30 newtons (N) and 70 N act on an object at angles of 45° and 120° with the positive x-axis, as shown in the figure. Find the direction and magnitude of the resultant force;
Two forces of magnitude 40 newtons (N) and 60 N act on an object at angles of 30° and -45° with the positive x-axis, as shown in the figure. Find the direction and magnitude of the resultant force;
A man pushes a wheelbarrow up an incline of 20° with a force of 100 pounds. Express the force vector F in terms of i and j.
A child pulls a wagon with a force of 40 pounds. The handle of the wagon makes an angle of 30° with the ground. Express the force vector F in terms of i and j.
Refer to problem 71. The points (-3,0, (-1,-2), (3,1) and (1,3) are the vertices of a parallelogram ABCD.(a) Find the new vertices of a parallelogram A'B'C'D' if it is translated by v = (3, -2).(b)
The field of computer graphics utilizes vectors to compute translations of points. For example, if the point (-3,2) is to be translated by v = (5,2), then the new location will be u' = u + v = (-3,2)
Find the direction angle of v for a given vector.v = -i + 3j
Find the direction angle of v for a given vector.v = -i - 5j
Find the direction angle of v for a given vector.v = 6i - 4j
Find the direction angle of v for a given vector.v = 4i - 2j
Find the direction angle of v for a given vector.v = -5i - 5j
Find the direction angle of v for a given vector.v = -3√3i + 3j
Find the direction angle of v for a given vector.v = i + √3j
Find the direction angle of v for a given vector.v = 3i + 3j
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 15, α = 315°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 25, α = 330°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 3, α = 240°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 14, α = 120°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 8, α = 45°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 5, α = 60°
If P = (-3, 1) and Q = (x,4), find all numbers x such that the vector represented by PQ(vector) has length 5.
If v = 2i - j and w = xi + 3j find all numbers x for which |v + w| = 5.
Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction
Find a vector v whose magnitude is 4 and whose component in the i direction is twice the component in the j direction.
Find the unit vector in the same direction as v. v = 2i - j
Find the unit vector in the same direction as v. v = i - j
Find the unit vector in the same direction as v. v = -5i + 12j
Find the unit vector in the same direction as v.v = 3i - 4j
Find the unit vector in the same direction as v. v = -3j
Find the unit vector in the same direction as v. v = 5i
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v | + |w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v | - |w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v + w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v - w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.3v - 2w
Find the quantity if v = 3i - 5j and w = -2i + 3j.2v + 3w
Find |v|. v = 6i + 2j
Find |v|. v = -2i + 3j
Find |v|. v = -i - j
Find |v|. v = i - j
Find |v|. v = -5i + 12j
Find |v|. v = 3i - 4j
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (1, 1); Q = (2, 2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (1, 0); Q = (0, 1)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (-1, 4); Q = (6, 2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (-2, -1); Q = (6, -2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (-3, 2); Q = (6, 5)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (3, 2); Q = (5, 6)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (0, 0); Q = (-3, -5)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (0, 0); Q = (3, 4)
Use the figure below. Determine whether the given statement is true or false. If |v| = 2, what is |-4v|? B C A K G H D
Use the figure below. Determine whether the given statement is true or false. If |v| = 4, what is |3v|? A ш
Use the figure at the right. Determine whether the given statement is true or false. A + B + C + H + G = 0
Use the figure at the right. Determine whether the given statement is true or false. A + B + K + G = 0
Evaluate the integral. (In x)²dx
Evaluate the integral. х сosh ax dx
Evaluate the integral. |t csc? t dt
Evaluate the integral. tan 2y dy -1
Evaluate the integral. tª In t dt
Evaluate the integral. S In Vr. (x dx
Evaluate the integral. cos x dx
Evaluate the integral. t2 sin ßt dt
Evaluate the integral. | (x2 + 2x) cos x dx
Evaluate the integral. | (х — 1) sin mxх dx
Evaluate the integral. -3t te dt
Evaluate the integral. Гуечз dy ,0.2y
Evaluate the integral. x cos 5x dx

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