. Leave no spaces between mathematical operators. For example, the line 2x + 5y = 10 should be typed in as "2x+5y=10." . Do not begin your solution with an equal sign. For example, the answer to the question "The sum of 2 and 5 is" should be typed in as "7", and not "=7". . The "A" (caret) symbol should be used to indicate exponents. For example, y = 5" would be entered as "y=5"x." . In the case of an expression use brackets. For example, y = (2X + 7)2 should be typed "y=(2x+7)"2" . No vector symbols are needed in your answers. For example 2G + 35 would be typed as "2u+3v". . Other common symbols include: o The "+" (division) symbol, which should be typed as "l" (backslash). For example would be typed as "x/(x-3)". Be sure to frame the 3 :133 numerator and denominator with brackets as necessary. 0 The "x" (multiplication or cross product) symbol, which should be typed as "*" (asterisk). For example 6 + 53 would be typed as "u*5v". o The "J" (square root) symbol, which should be typed as "root". For example y = 333 | 2 would be typed as "root(x"3+2)". o The "l'l" (pi) symbol, which should be typed as "pi". For example -7|'| would be typed as "-7pi". Question 1 (1 point) Given three vectors, u, V, and w, if u . V W = 0, what geometrical result can be concluded? O u, v and w are on the same plane O vand w, are parallel, and both are perpendicular to u O u, v and w are mutually perpendicular O One of u, v or w must be 0.Which of the following vectors is not perpendicular to vector u = (-5, 2, 1) ? Ov= (3, 7, 1) Ov= (-2, - 10, 10 Ov = (4, 5, 8 Ov = (1, 2, 1)Question 3 (1 point) The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has equation 3x + z - 13 = 0 Ox - 7y - 3z + 13 = 0 4x + 2y +z - 5 =0 O 2x - y - 62 = 0Question 4 (1 point) If Car A is travelling north at 50 km/h and Car B is travelling south at 60 km/h, the velocity of Car A relative to Car B is Q 110 km/h south Q 10 km/h north Q 110 km/h north 0 10 km/h south Question 5 (1 point) > > > If 'u, , 'U and 'w are mutually perpendicular vectors, which of the following would not be true? Question 6 (1 point) > > Suppose u and 'U are non-zero, parallel vectors. Which of the following could not possibly be true? _> OZ+?=0 2 03m: Fl Question 7 (1 point) > > . To the nearest tenth, the angle between p = (1, -5) and 'U = (4, 6) IS : AJ Question 8 (1 point) > For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates a, Question 9 (1 point) _> > The cross product of vectors 0,: (-1, 4, 6) and b = (3, 0, -2) is A'/ Question 10 (1 point) If the point (4, 4, g) is on the line (x, y, z) = (8,0, 2) + t(1, 1, 3), the value of g is A ( ] Question 11 (1 point) > > _ The dot product of vectors p = (3, -5) and q = (15,9) IS :] r Question 12 (1 point) I The vector; = (3, 4) is projected onto the x-axis The length of the projection is l: \"v Question 13 (3 points) Find the equation of the following lines in the required form: 1. through the points P(1, -3, 2) and Q(9, 2, 0) [vector equation] _> 2. with direction vector d = (5, 3, -4) and z-intercept 7 [symmetric equations] 3. through T(2, -5) and perpendicular to the line 3x - 6y = 5 [scalar equation] Blank # 1 Blank # 3 Question 14 (1 point) The length/magnitude of the vector c = (2, -3, 1) is A/ Question 15 (1 point) If m = (2, 1, 5) and n = (3, 0, x) are perpendicular, then the value of x is A/