JEE Mains · Physics · STD 11 - 3.1 vectors
If two vectors \(\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}\) and \(\vec{Q}=4 \hat{i}-2 \hat{j}+ mk\) are perpendicular to each other. Then, the value of \(m\) will be :
- A \(1\)
- B \(-1\)
- C \(-3\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ P } \cdot \overrightarrow{ Q }=0\) \((\hat{i}+2 m \hat{j}+m \hat{k}) \cdot(4 \hat{i}-2 \hat{j}+m \hat{k})=0\) \(\Rightarrow 4-4 m+m^2=0\) \(\Rightarrow( m -2)^2=0 \Rightarrow m=2\)
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