a1i^+a2j^ is a unit vector perpendicular to 4i^−3j^ if

Dot product to be zeroa 4a1−3a2=0→(1)a1i^+a2j^ is unit vectora12+a22=1→(2)Solve (1), (2)a1=0.6, a2=0.8

a1i^+a2j^ is a unit vector perpendicular to 4i^−3j^ if

Dot product to be zeroa 4a1−3a2=0→(1)a1i^+a2j^ is unit vectora12+a22=1→(2)Solve (1), (2)a1=0.6, a2=0.8

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

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$a_{1} = 0.8, a_{2} = 0.6$

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

$a_{1} = 0.6, a_{2} = 0.8$

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

answer is A.

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Detailed Solution

Dot product to be zero

$(a)$ $4 a_{1} - 3 a_{2} = 0 \to (1)$

$a_{1} \hat{i} + a_{2} \hat{j}$ is unit vector

$\sqrt{a_{1}^{2} + a_{2}^{2}} = 1 \to (2)$

Solve (1), (2)

$a_{1} = 0.6, a_{2} = 0.8$

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