MHT CET · Maths · Vector Algebra
If \(\overline{\mathrm{a}}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{\mathrm{k}})\) and \(\overline{\mathrm{b}}=\frac{1}{7}(2 \hat{i}+3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}})\) then the value of \((2 \bar{a}-\bar{b}) \cdot[(\bar{a} \times \bar{b}) \times(\bar{a}+2 \bar{b})]=\)
- A \(\frac{1}{5}\)
- B \(-5\)
- C \(5\)
- D \(-\frac{1}{5}\)
Answer & Solution
Correct Answer
(B) \(-5\)
Step-by-step Solution
Detailed explanation
\(|\overline{\mathrm{a}}|^2 = \frac{1}{10}(3^2+1^2) = 1\) \(|\overline{\mathrm{b}}|^2 = \frac{1}{49}(2^2+3^2+(-6)^2) = 1\)
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