The vectors overrightarrow P = ahat i + ahat | vedclass

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Question

(A) Two vectors are perpendicular if their dot product is zero,i.e.,$\overrightarrow P \cdot \overrightarrow Q = 0$.Given $\overrightarrow P = a\hat i

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$3$

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(A) Two vectors are perpendicular if their dot product is zero,i.e.,$\overrightarrow P \cdot \overrightarrow Q = 0$.Given $\overrightarrow P = a\hat i + a\hat j + 3\hat k$ and $\overrightarrow Q = a\hat i - 2\hat j - \hat k$.Calculating the dot product: $(a)(a) + (a)(-2) + (3)(-1) = 0$.This simplifies to: $a^2 - 2a - 3 = 0$.Factoring the quadratic equation: $(a - 3)(a + 1) = 0$.This gives $a = 3$ or $a = -1$.Since the question asks for the positive value of $a$,we have $a = 3$.

The vectors $\overrightarrow P = a\hat i + a\hat j + 3\hat k$ and $\overrightarrow Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other. The positive value of $a$ is

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