How do you find the unit vector having the same direction as vector v = 2i - j + k?

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How do you find the unit vector having the same direction as vector v = 2i - j + k?

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Answer 1 · 2016-07-13T17:13:16

The unit vector having the same direction as $v$ $v$ will be $\frac{2}{\sqrt{6}} i - \frac{1}{\sqrt{6}} j + \frac{1}{\sqrt{6}} k$ $2/sqrt6i-1/sqrt6j+1/sqrt6k$

Explanation:

For a vector $v = a i + b j + c k$ $v=ai+bj+ck$ , unit vector in the same direction is given by $\frac{v}{| v |}$ $v/(|v|)$ , where $| v | = \sqrt{a^{2} + b^{2} + c^{2}}$ $|v|=sqrt(a^2+b^2+c^2)$ .

Hence for $v = 2 i - j + k$ $v=2i-j+k$ , as $| v | = \sqrt{2^{2} + {(- 1)}^{2} + 1^{2}}$ $|v|=sqrt(2^2+(-1)^2+1^2)$

= $\sqrt{4 + 1 + 1} = \sqrt{6}$ $sqrt(4+1+1)=sqrt6$

Hence. the unit vector having the same direction as $v$ $v$ will be

$\frac{2}{\sqrt{6}} i - \frac{1}{\sqrt{6}} j + \frac{1}{\sqrt{6}} k$ $2/sqrt6i-1/sqrt6j+1/sqrt6k$

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How do you find the unit vector having the same direction as vector v = 2i - j + k?

1 Answer

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