JEE Mains · Maths · STD 12 - 10. vector algebra
If the projection of the vector \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) on the sum of the two vectors \(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}\) and \(-\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is \(1,\) then \(\lambda\) is equal to ..... .
- A \(8\)
- B \(7\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=\hat{i}+2 \hat{j}+\hat{k}\) \(\vec{b}=(2-\lambda) \hat{i}+6 \hat{j}-2 \hat{k}\) \(\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=1, \vec{a} \cdot \vec{b}=12-\lambda\) \((\vec{a} \cdot \vec{b})=|\vec{b}|^{2}\) \(\lambda^{2}-24 \lambda+144=\lambda^{2}-4 \lambda+4+40\)…
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