Question

Let u = (1, 2 -2), v= (2, 1, 3) and w = j + 4k. a) Find cos theta, where theta is the angle in degrees between u and w.

Answer 1

Answer: The value of cos theta is -0.352.

Explanation:

Since we have given that

We need to find the cos theta between u and w.

As we know the formula for angle between two vectors.

`\cos\ \theta=\frac{\vec{u}.\vec{w}}{\mid u\mid \mid w\mid}`

So, it becomes,

`\cos \theta=(2-8)/(√(1^2+2^2+(-2)^2)√(1^2+4^2))\\\\\cos \theta=(-6)/(√(17)√(17))=(-6)/(17)=-0.352\\\\\theta=\cos^(-1)((-6)/(17))=110.66^\circ`

Hence, the value of cos theta is -0.352.