Question

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

Answer 1

unit vector = vector / magnitude
therefore
unit vector =2i-3j+4k/ sqroot (2)^2+(3)^2+(4)^2
unit vector =2/sqroot29 i - 3/sqroot29 j + 4/sqroot29 k

Answer 2

A unit vector is a vector that has a magnitude of 1. Or. Any vector can become a unit vector by dividing it by the vector's magnitude.

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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