Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. u: (1,1), (6,11) v: (-2,5), (3,15) u= 10i-5j, v = 10i+5j which are equivalent u= i+10j, v = 10Oi + 5j which are not equivalent u= 5i+10j, v = 5i+10j which are equivalent u= 5i-10j, v= - 5i-10j which are equivalent Ou= - 5i+10j, v = - 5i+10j which are equivalent

Either a triangle whose vertices are A(-2, -1, 3), B(7, 8, -4) and C(5, 0, 2). Using an operation on vectors, determine if the triangle is rectangular.

Please assit me.

For the given vectors u and v, find the cross product u x v. +- (²-₁-1-3) u x V = u = (-2, 6, 3), v =

The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)

The figure below shows two named points A and B in R?. 6 4 A -1 -2 -3 -4 B -5 -6 -6 -5 -4 -3 -2 -1 5 6 1 3 4 > Part 1 Part 2 a. Write the vector BA as a sum of two vectors, one parallel to (1,0) and the other parallel to (0, -2). ВА- + b. Write the vector BA as a sum of two vectors, one parallel to (1, 1) and the other parallel to (-1, 1). BA = +

Use these 3 vectors ?⃗ = (-2, -12, 4), ? = (3, -2, 1), ?⃗ = (8, 12, -4) to verify the the associative property

Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4, 1)} (a) u = (6, 25, -20, -3) J: + (3 u = -1 52 (b) -10, 2) 3 -- F1 + 4 52 2 (c) 57 w = -4, -14, -)- 7 13 4 = (14, -3, 7, (d) 41 z = b1 + $2

17) Let a = [3, -4] and b = [−6, k]. a) Determine the value(s) of k such that a + b = a + 6. What is the relationship between the two vectors for this result to be true? b) Determine the value(s) of k such that a + b < a + b. What is the relationship between the two vectors for this result to be true?

Illustrate with an example and a diagram why a+b=6+a¯ for all vectors a and b