JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k\) and \(\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k\) be three vectors such that the projection vector of \(\vec b\) on \(\vec a\) is \(\vec a\). If \(\vec a\, + \vec b\) is perpendicular to \(\vec c\) , then \(\left| {\vec b} \right|\) is equal to
- A \(\sqrt {22}\)
- B \(4\)
- C \(\sqrt {32}\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
Projection of \(\overrightarrow{\mathrm{b}}\) on \(\overrightarrow{\mathrm{a}}=\frac{\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}}{|\overrightarrow{\mathrm{a}}|}=|\overrightarrow{\mathrm{a}}|\) \(\Rightarrow \mathrm{b}_{1}+\mathrm{b}_{2}=2\) .....\((1)\) and…
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