Vector magnitude

Classical Mechanics Level 1

Find the unit vector in the direction of 5 i + j − 2 k . 5 i +j - 2 k.

5 i + j − 2 k 5 i + j - 2 k 5 30 i + 1 30 j − 2 30 k \frac{5}{30}i+\frac{1}{30}j-\frac{2}{30} k 5 30 i + 1 30 j − 2 30 k \frac{5}{\sqrt{30}}i+\frac{1}{\sqrt{30}}j-\frac{2}{\sqrt{30}} k None of the above

Rohit Nair by Rohit Nair , 21, India

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1 solution

Benja Vera
Jun 22, 2019

In general, the (only!) unit vector parallel to a nonzero vector v ⃗ \vec{v} is given by v ^ = v ⃗ ∥ v ⃗ ∥ \hat{v} = \frac{\vec{v}}{\|\vec{v}\|} In this case the magnitude evaluates to 5 2 + 1 2 + ( − 2 ) 2 = 30 \sqrt{5^2 + 1^2 + (-2)^2} = \sqrt{30} so it follows that the solution is v ^ = 5 30 i ^ + 1 30 j ^ − 2 30 k ^ \hat{v} = \frac{5}{\sqrt{30}}\hat{i} + \frac{1}{\sqrt{30}}\hat{j} - \frac{2}{\sqrt{30}}\hat{k}

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