Vector Math

Level 1

A grid in three dimensions consists of two vectors: A and B

A = 6i -2j +2k

B = -i+2j+5k

What is the angle between the two lines at the point where they intersect?

2 solutions

Rohan Chandra
Jan 20, 2014

Let the angle be simply,"a" :

Cos (a) = (A . B) / (|A| x |B|)

Since (A . B) = 0 (Dot Prod.)

Cos a = 0

Cos-1 (0) = $\boxed{90}$

Raghav Dua
Jan 20, 2014

To find the angle x , we use:

Cos (x) = (A . B) / (|A| x |B|)

where (A . b) is the Dot Product of A and B; |A| is the Magnitude of the vector A

Since (A . B) = 0, the whole expression becomes 0. This, we have:

Cos (x) = 0

Cos-1 (0) = 90

Thus, answer is 90 degrees