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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.

User Hsluoyz
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1 Answer

3 votes

Answer: The value of cos theta is -0.352.

Explanation:

Since we have given that


\vec{u}=1\hat{i}+2\hat{j}-2\hat{k}\and\\\\\vec{w}=\hat{j}+4\hat{k}

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.

User Jonathan Myers
by
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