Topic: Engineering Mathematics
If two vectors $\vec{a}=3\hat{i}+4\hat{j}-7\hat{k}$ and $\vec{b}=P\hat{i}-6\hat{j}+3\hat{k}$ are perpendicular, the value of P is
- A. 1
- B. 0
- C. 12
- D. 15
Answer: D. 15
Explanation: If two vectors are perpendicular, their dot product is zero. $\vec{a} \cdot \vec{b} = (3\hat{i}+4\hat{j}-7\hat{k}) \cdot (P\hat{i}-6\hat{j}+3\hat{k}) = 0$. $\Rightarrow 3P + 4(-6) + (-7)(3) = 0 \Rightarrow 3P - 24 - 21 = 0 \Rightarrow 3P = 45 \Rightarrow P = 15$.