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Geometry Level 1

Which vector represents the unit vector in the direction of ⟨ 3 , − 6 , 2 ⟩ \langle 3, -6, 2\rangle ?

i + j + k i + j + k 3 49 i − 6 49 j + 2 49 k \frac{3}{49}i - \frac{6}{49}j + \frac{2}{49}k i − j + k i - j + k 3 7 i − 6 7 j + 2 7 k \frac{3}{7}i - \frac{6}{7}j + \frac{2}{7}k

Andrew Ellinor by Andrew Ellinor , 33, USA

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1 solution

Andrew Ellinor
Sep 30, 2015

In order to obtain a unit vector, you must divide each component by that vector's magnitude. First, let's compute the magnitude of the given vector: ∥ ⟨ 3 , − 6 , 2 ⟩ ∥ = 3 2 + ( − 6 ) 2 + 2 2 = 7. \|{\langle3, -6, 2\rangle}\| = \sqrt{3^2 + (-6)^2 + 2^2} = 7.

Dividing each component by 7 gives us ⟨ 3 7 , − 6 7 , 2 7 ⟩ which is equivalent to 3 7 i − 6 7 j + 2 7 k \langle \frac{3}{7}, -\frac{6}{7}, \frac{2}{7}\rangle \text{ which is equivalent to } \frac{3}{7}i - \frac{6}{7}j + \frac{2}{7}k

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