How do you find the unit vector in the direction of the given vector 6i-2j?

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How do you find the unit vector in the direction of the given vector 6i-2j?

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Answer 1 · 2016-10-29T18:43:46

$(3 \frac{\sqrt{10}}{10}) ˆ i - (\frac{\sqrt{10}}{10} ˆ j)$ $(3sqrt(10)/10)hati - (sqrt(10)/10hatj)$ Please read the explanation.

Explanation:

Divide the given vector by the magnitude:

$∣ ∣ 6 ˆ i - 2 ˆ j ∣ ∣ = \sqrt{6^{2} + {(- 2)}^{2}} = 2 \sqrt{10}$ $|6hati - 2hatj| = sqrt(6^2 + (-2)^2) = 2sqrt(10)$

$\frac{6 ˆ i - 2 ˆ j}{2 \sqrt{10}} = (3 \frac{\sqrt{10}}{10}) ˆ i - (\frac{\sqrt{10}}{10}) ˆ j)$ $(6hati - 2hatj)/(2sqrt(10)) = (3sqrt(10)/10)hati - (sqrt(10)/10)hatj)$

Please observe that the magnitude of the resulting vector is 1:

$\sqrt{{(3 \frac{\sqrt{10}}{10})}^{2} + {(- (\frac{\sqrt{10}}{10}) ˆ j)}^{2}} = 1$ $sqrt((3sqrt(10)/10)^2 + (- (sqrt(10)/10)hatj)^2) = 1$

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How do you find the unit vector in the direction of the given vector 6i-2j?

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