JEE Mains · Maths · STD 12 - 10. vector algebra
If \( \overrightarrow{ a }=2 \hat{ i }+\hat{ j }+3 \hat{ k }, \overrightarrow{ b }=3 \hat{ i }+3 \hat{ j }+\hat{ k } \) and \(\overrightarrow{ c }= c _{1} \hat{ i }+ c _{2} \hat{ j }+ c _{3} \hat{ k }\) are coplanar vectors and \(\overrightarrow{ a } \cdot \overrightarrow{ c }=5, \overrightarrow{ b } \perp \overrightarrow{ c }\), then \(122\left( c _{1}+ c _{2}+ c _{3}\right)\) is equal to.......
- A \(150\)
- B \(157\)
- C \(159\)
- D \(190\)
Answer & Solution
Correct Answer
(A) \(150\)
Step-by-step Solution
Detailed explanation
\(\overline{ a } \cdot \overline{ c }=5 \Rightarrow 2 c _{1}+ c _{2}+3 c _{3}=5\)..........\((1)\) \(\overline{ b } \cdot \overline{ c }=0 \Rightarrow 3 c _{1}+3 c _{2}+ c _{3}=0\).............\((2)\) And…
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