TS EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three independent vectors and there exists a non zero scalar traid \((l, m, n)\) such that \(l(3 \mathbf{a}+2 \mathbf{b}+\mathbf{c})+m(2 \mathbf{a}+2 \mathbf{b}+3 \mathbf{c})\) \(+n(\mathbf{a}+2 \mathbf{b}+5 \mathbf{c})=\mathbf{0}\), then
- A \(l=m=n\)
- B \(l=n\)
- C \(l=n, m+2 n=0\)
- D \(m+2 n=0,1+n=0\)
Answer & Solution
Correct Answer
(C) \(l=n, m+2 n=0\)
Step-by-step Solution
Detailed explanation
Given, \(l(3 \mathbf{a}+2 \mathbf{b}+\mathbf{c})+m(2 \mathbf{a}+2 \mathbf{b}+3 \mathbf{c})+n(\mathbf{a}+2 \mathbf{b}+5 \mathbf{c})=0\) Where \(l, m, n\) are scalar \(\therefore \mathbf{a}(3 l+2 m+n)+2 \mathbf{b}(l+m+n)+\mathbf{c}(l+3 m+5 n)=0\)…
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