Question

find the unit vector in direction of 2i-3j+4k

Answer 1

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Here's your answer...

The unit vector can ne found by dividing the given vector with its magnitude.

Magnitude of 2i-3j+4k
$= \sqrt{ {2}^{2} + {3}^{2} + {4}^{2} } \\ = \sqrt{4 + 9 + 16 } \\ = \sqrt{29}$
Dividing the given vector by the magnitude...

$\frac{2i - 3j + 4k}{ \sqrt{29} } \\ = \frac{2}{ \sqrt{29} } i - \frac{3}{ \sqrt{29} } j + \frac{4}{ \sqrt{29} } k$
This is the unit vector needed.

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Answer 2

unit vector A=A vector/magnitude of A
=2i-3j+4k/root 4+9+16
=2i-3j+4k /root 29