AP EAMCET · Maths · Vector Algebra
If the vectors \(a \hat{i}+\hat{j}+3 \hat{k}, 4 \hat{i}+5 \hat{j}+\hat{k}\), and \(4 \hat{i}+2 \hat{j}+6 \hat{k}\), are coplanar, then \(a=\)
- A \(2\)
- B \(1\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(a \hat{i}+\hat{j}+3 \hat{k}, 4 \hat{i}+5 \hat{j}+\hat{k} \text { and } 4 \hat{i}+2 \hat{j}+6 \hat{k}\) are coplanar then \(\left|\begin{array}{lll} a & 1 & 3 \\ 4 & 5 & 1 \\ 4 & 2 & 6 \end{array}\right|=0 \Rightarrow 18 a-36=0 \Rightarrow a=2\)
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