Given P→=3i^−4j^. Which of the following is perpendicular to P→?

P→ is in the fourth quadrant. 4i^+3j^ is in the first quadrant. Clearly, 4i^+3j^ can be perpendicular to P→. For confirmation, let us check whether their dot product is zero.3i^-4j^4i^+3j^=12-12=0This shows that 4i^+3j^ is perpendicular to 3i^-4j^ .

Given P→=3i^−4j^. Which of the following is perpendicular to P→?

P→ is in the fourth quadrant. 4i^+3j^ is in the first quadrant. Clearly, 4i^+3j^ can be perpendicular to P→. For confirmation, let us check whether their dot product is zero.3i^-4j^4i^+3j^=12-12=0This shows that 4i^+3j^ is perpendicular to 3i^-4j^ .

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Given $\vec{P} = 3 \hat{i} - 4 \hat{j}$ . Which of the following is perpendicular to $\vec{P}$ ?

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$4 \hat{i} + 3 \hat{j}$

$4 \hat{i}$

$3 \hat{i}$

$4 \hat{i} - 3 \hat{j}$

answer is C.

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Detailed Solution

$\vec{P}$ is in the fourth quadrant. $4 \hat{i} + 3 \hat{j}$ is in the first quadrant. Clearly, $4 \hat{i} + 3 \hat{j}$ can be perpendicular to $\vec{P}$ . For confirmation, let us check whether their dot product is zero.