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lesya692 [45]
3 years ago
11

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.

Mathematics
1 answer:
vodka [1.7K]3 years ago
8 0

Answer: The value of cos theta is -0.352.

Step-by-step 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=\dfrac{\vec{u}.\vec{w}}{\mid u\mid \mid w\mid}

So, it becomes,

\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

Hence, the value of cos theta is -0.352.

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{ \sf{x =  \frac{ - 5± \sqrt{35 {i}^{2} } }{10} }} \\  \\  = { \sf{x =   \frac{ - 5±i \sqrt{35} }{10} }}

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