JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\quad \overrightarrow{ a }=\alpha \hat{ i }+3 \hat{ j }-\hat{ k }, \overrightarrow{ b }=3 \hat{ i }-\beta \hat{ j }+4 \hat{ k } \quad\) and \(\overrightarrow{ c }=\hat{ i }+2 \hat{ j }-2 \hat{ k }\) where \(\alpha, \beta \in R\), be three vectors. If the projection of \(\vec{a}\) on \(\vec{c}\) is \(\frac{10}{3}\) and \(\overrightarrow{ b } \times \overrightarrow{ c }=-6 \hat{ i }+10 \hat{ j }+7 \hat{ k }\), then the value of \(\alpha+\beta\) equal to
- A \(3\)
- B \(4\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(\frac{\overrightarrow{ a } \cdot \overrightarrow{ c }}{|\overrightarrow{ c }|}=\frac{10}{3}\) \(\Rightarrow \frac{\alpha+6+2}{\sqrt{1+4+4}}=\frac{10}{3} \Rightarrow \alpha=2\) and…
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