Answer: The value of cos theta is -0.352.
Step-by-step explanation:
Since we have given that
[tex]\vec{u}=1\hat{i}+2\hat{j}-2\hat{k}\and\\\\\vec{w}=\hat{j}+4\hat{k}[/tex]
We need to find the cos theta between u and w.
As we know the formula for angle between two vectors.
[tex]\cos\ \theta=\dfrac{\vec{u}.\vec{w}}{\mid u\mid \mid w\mid}[/tex]
So, it becomes,
[tex]\cos \theta=\dfrac{2-8}{\sqrt{1^2+2^2+(-2)^2}\sqrt{1^2+4^2}}\\\\\cos \theta=\dfrac{-6}{\sqrt{17}\sqrt{17}}=\dfrac{-6}{17}=-0.352\\\\\theta=\cos^{-1}(\dfrac{-6}{17})=110.66^\circ[/tex]
Hence, the value of cos theta is -0.352.
