Question

Two vectors are given by a = i - 5j and b = -4i + j. What is the unit vector of the direction of a b?

a. i + 2j
b. -3i - 6j
c. 2i - 7j
d. 3i + 4j

Answer 1

To find the unit vector of the direction of a x b, calculate the cross product of vectors a and b, and find the magnitude of the resulting vector. Then, divide the resulting vector by its magnitude to get the unit vector.

Step-by-step explanation:

To find the unit vector of the direction of a x b, we need to calculate the cross product of vectors a and b, and then find the magnitude of the resulting vector. Here's how:

First, calculate the cross product: a x b = (1)(1) - (-5)(-4) = 1 - 20 = -19.

Next, find the magnitude of the resulting vector: |a x b| = √((-19)²) = √(361) = 19.

Finally, divide the resulting vector by its magnitude to get the unit vector: -19/19.