JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k}\) and \(\vec{b}=3 \hat{i}-5 \hat{j}+4 \hat{k}\) be two vectors, such that \(\vec{a} \times \vec{b}=-\hat{i}+9 \hat{i}+12 k\). Then the projection of \(\vec{b}-2 \vec{a}\) on \(\vec{b}+\vec{a}\) is equal to.
- A \(2\)
- B \(\frac{39}{5}\)
- C \(9\)
- D \(\frac{46}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{46}{5}\)
Step-by-step Solution
Detailed explanation
Let \(\vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}+4 \hat{k}\) \(\vec{a} \times \vec{b}=-\hat{i}+9 \hat{j}+12 \hat{k}\) \(\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ \alpha & 1 & \beta \\ 3 & -5 & 4\end{array}\right|\)…
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