JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(a, b\) and \(c\) be distinct positive numbers. If the vectors \(a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k}\) and \(c \hat{i}+c \hat{j}+b \hat{k}\) are co-planar, then \(\mathrm{c}\) is equal to:
- A \(\sqrt{a b}\)
- B \(\frac{a+b}{2}\)
- C \(\frac{1}{a}+\frac{1}{b}\)
- D \(\frac{2}{\frac{1}{a}+\frac{1}{b}}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{a b}\)
Step-by-step Solution
Detailed explanation
Hence \(\left|\begin{array}{lll}a & a & c \\ 1 & 0 & 1 \\ c & c & b\end{array}\right|=0\) \(\Rightarrow c^{2}=a b \Rightarrow c=\sqrt{a b}\)
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