MHT CET · Maths · Vector Algebra
If the projection of \(\bar{a}\) on \(\bar{b}+\bar{c}\) is twice the projection of \(\bar{b}+\bar{c}\) on \(\bar{a}\) also if \(|\bar{b}|=2 \sqrt{2},|\bar{c}|=4\) and the angle between \(\bar{b}\) and \(\bar{c}\) is \(\frac{\pi}{4}\) then \(|\bar{a}|=\)
- A \(2 \sqrt{10}\)
- B \(3 \sqrt{10}\)
- C \(4 \sqrt{10}\)
- D \(5 \sqrt{10}\)
Answer & Solution
Correct Answer
(C) \(4 \sqrt{10}\)
Step-by-step Solution
Detailed explanation
\(\frac{\bar{a} \cdot (\bar{b}+\bar{c})}{|\bar{b}+\bar{c}|} = 2 \frac{(\bar{b}+\bar{c}) \cdot \bar{a}}{|\bar{a}|}\) \(|\bar{a}| = 2 |\bar{b}+\bar{c}|\)
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