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cross product two same vectors always zero
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a) 30 - 5V._b) 2V - W'. 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculato
finall answers Consider the following. u = (-6, 6), v = (1, -1) (a) Find u. v. u. V (b) Find the angle between u and v to the nearest degree. Submit Answer 3. -/2 POINTS SPRECALC7 9.2.010.MI. 0/2 Submissions Used Consider the following. u = 4i + j, v = 5i - 2j (a) Find u. v. u.v= (b) Find the angle between u and v to the nearest degree. A = Submit Assign Type here to search
U can show both but i only need b 7. Let u = (1,2,1) and v (1,0,-1). Find (a) u x v Marks 13 O I b) v.(ux v
the plane PQ X PR 1. Find unit vector the perpendicular to P(1,1,1), Q(2,1,3), R(2, 2, 1).
Directions: In 25-27, let u = 15-6i .V=-5+ 4i, and w=-2-i. [25] Simplify u + 3v: A) -6i B) 6i C) 30-6i D) 30+6i E) none of these [26] Find the sum of the conjugate of v and the conjugate of w. A)-7-31 B) -7 +31 C) 7-3i D) 7+3i E) none of these [27] Subtract w from u. A) -17-71 B) -17+5i c) 13-5i D) 13-71 E) none of these
Carefully draw the line segment PQ that connects P=(4, 5, -3) and Q=(0, -4, 2) . Include dotted vertical lines from the xy-plane to P and Q to show perspective. Find the distance between P and Q, from the previous problem. Then find the coordinates of the midpoint of the line segment PQ . Let u= -3i+5j+7k and v= 10i+j-2k . Show that u × v is orthogonal to the vector v .
Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-5, 3, 5), Q(-3, 6, 8), R(-6, 2, 4), S(1, 1, 7).
Fourth Homework (1) Let P-(**.0) and Q ( . (a) Find the pole of the line PQ (b) Find the parametrization of the line PQ (c) Does (ch,顽週lie on the line PQ? 克,2 7, ) lie on the line PQ? (2) Find the distance between the lines (1,0,-1) + t(2,3,0) and m (2,-1,3) +s(0, 1,2). (3) Let A and B be two distinct points of S2. Show that X e I d(X, A) = d(X, b)) is a line and...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [ 3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ] (i) Calculate A + B, (ii) Calculate AB (iii) Calculate the inverse of B, (iv) Calculate the determinant of C. (b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2) and (5, −1, 4) respectively. (i) Show that P Q~ =...