JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}\) be a vector which is perpendicular to the vector \(3 \hat{ i }+\frac{1}{2} \hat{ j }+2 \hat{ k }\). If \(\overrightarrow{ a } \times(2 \hat{ i }+\hat{ k })=2 \hat{ i }-13 \hat{ j }-4 \hat{ k }\), then the projection of the vector \(\vec{a}\) on the vector \(2 \hat{ i }+2 \hat{ j }+\hat{ k }\) is
- A \(\frac{1}{3}\)
- B \(1\)
- C \(\frac{5}{3}\)
- D \(\frac{7}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{3}\)
Step-by-step Solution
Detailed explanation
\((\vec{a} \times(2 \hat{i}+\hat{k})) \times\left(3 \hat{i}+\frac{1}{2} \hat{j}+2 \hat{k}\right)\) \(=(2 \hat{i}-13 \hat{j}-4 \hat{k}) \times\left(3 \hat{i}+\frac{1}{2} \hat{j}+2 \hat{k}\right)\)…
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