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While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 121 m at an angle 0 = 30.0 north of east, and 169 m south. Find the resultant displacement from the cave entrance. The figure below suggests the situation but is not drawn to scale. magnitude m direction . south of east Cave W -DE Final un- entrance positionConsider the three displacement vectors A = (-51 - 3j) m, B = (91 - 8j) m, and C = (1i + 5j) m. Use the component method to determine the following. (a) The magnitude and direction of the vector D = A + B + C. magnitude m direction counterclockwise from the +x axis (b) The magnitude and direction of E = -A - B + C. magnitude m direction counterclockwise from the +x axisGiven the displacement vectors A = (1.00 i - 5.00 j + 6.00 k) m and B = (3.00 i + 2.00 j - 9.00 k) m, find the magnitudes of the following vectors and express each in terms of its rectangular components. (a) C = A +B ICI = m C = ( i + k ) m (b) D = 2A - B IDI = m i + j + k ) mThe vector A has x, y, and z components of -7.00, -4.00, and 1.00 units, respectively. (a) Write a vector expression for A in unit-vector notation. A (b) Obtain a unit-vector expression for a vector B one-fourth the length of A pointing in the same direction as A. B = () Obtain a unit-vector expression for a vector C three times the length of A pointing in the direction opposite the direction of A. =Vector B has x, y, and z components of 6.00, 8.00, and 4.00 units, respectively. Calculate the magnitude of B. Calulcate the angle that B makes with the x axis. Calculate the angle that B makes with the y axis. Calculate the angle that B makes with the z axis.Vector A has a negative x component 2.80 units in length and a positive y component 2.40 units in length. (a) Determine an expression for A in unit-vector notation. + j) units (b) Determine the magnitude and direction of A. magnitude unit(s) direction counterclockwise from the positive x axis (c) What vector B when added to vector A, gives a resultant vector with no x component and a negative y component 4.32 units in length? i+ [ j) unitsThree displacement vectors of a croquet ball are shown in the figure, where IKI = 19.0 units, IEI = 60.0 units, and C = 45.0 units. {a} Find the resultant in unit-vector notation. _, R = [b] Find the magnitude and direction of the resultant displacement. units 0 (from the +x axis} The figure below illustrates typical proportions of male (m) and female (f) anatomies. The displacements d , and d from the soles of the feet to the navel have magnitudes of 100 cm and 83.5 cm, respectively. The displacements d , and d , from the navel to outstretched fingertips have magnitudes of 99 cm and 84.5, respectively. Find the vector sum of these displacements d ? = d , + d 2 for both people. for the male magnitude cm direction above the +x axis (first quadrant) for the female magnitude cm direction . above the +x axis (first quadrant) ed2m 23.0 do 28.0 dim dif