JEE Mains · Maths · STD 12 - 10. vector algebra
For three unit vectors \(\vec{a}, \vec{b}, \vec{c}\) satisfying \({|\vec{a}-\vec{b}|^{2}}+{|\vec{b}-\vec{c}|^{2}}+{|\vec{c}-\vec{a}|^{2}}=9\) and \({|2\vec{a}+k\vec{b}+k\vec{c}|}=3\), the positive value of k is:
- A 3
- B 6
- C 4
- D 5
Answer & Solution
Correct Answer
(D) 5
Step-by-step Solution
Detailed explanation
\({|\vec{a}-\vec{b}|^{2}}+{|\vec{b}-\vec{c}|^{2}}+|\vec{c}-\vec{a}|^{2}=9\) \(\Rightarrow \vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}=-\frac{3}{2}\) \(\Rightarrow \vec{a}+\vec{b}+\vec{c}=0 \Rightarrow \vec{b}+\vec{c}=-\vec{a}\) \({|2\vec{a}+k(\vec{b}+\vec{c})|}=3\)…
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