AP EAMCET · Maths · Vector Algebra
For some real number \(\lambda\), if the area of the triangle having \(\vec{a}=3 \hat{i}-\hat{j}+\lambda \hat{k}\) and \(\vec{b}=\lambda \hat{i}+\hat{j}-3 \hat{k}\) as two of its sides is \(\frac{\sqrt{195}}{2}\), then the number of distinct possible values of \(\lambda\) is
- A 4
- B 3
- C 2
- D 1
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\(\vec{a}=3 \hat{i}-\hat{j}+\lambda \hat{k}\) and \(\vec{b}=\lambda \hat{i}+\hat{j}-3 \hat{k}\) Area of the triangle \(=\frac{\sqrt{195}}{2}\) \(\Rightarrow \frac{1}{2}|\vec{a} \times \vec{b}|=\frac{1}{2} \sqrt{195} \Rightarrow|\vec{a} \times \vec{b}|^2=195\) ...(i) Now,…
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