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Test for Collinearity of Vectors

a1i+a2j is a ...

Question

$a_{1} i + a_{2} j$ is a unit vector perpendicular to 4i-3j if

A

a_{t} = .6, a_{2} = .8

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B

a_{1} = 3, a_{2} = 4

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C

a_{1} = .8, a_{2} = .6

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D

a_{1} = 4, a_{2} = 3

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Solution

The correct option is A $a_{t} = .6, a_{2} = .8$
$a_{1} i + a_{2} j$ is a unit vector perpendicular to $4 i - 3 j$
Therefore, $4 a_{1} - 3 a_{2} = 0$ ....(1)
Given that $\sqrt{{a_{1}}^{2} + {a_{2}}^{2}} = 1$ ....(2)
Solving (1) and (2): $a_{1} = 0.6$ and $a_{2} = 0.8$

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