AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}+x \mathbf{b}+y \mathbf{c}=\mathbf{0}\), \(\mathbf{a} \times \mathbf{b}+\mathbf{b} \times \mathbf{c}+\mathbf{c} \times \mathbf{a}=6(\mathbf{b} \times \mathbf{c})\), then the locus of the point \((x, y)\) is
- A \(x^2+y^2=1\)
- B \(x+y-5=0\)
- C \(2 x+6 y=5\)
- D \(x+y+6=0\)
Answer & Solution
Correct Answer
(B) \(x+y-5=0\)
Step-by-step Solution
Detailed explanation
Given, \[ \mathbf{a}+x \mathbf{b}+y \mathbf{c}=\mathbf{0} \] As we know that, if \(\mathbf{a}+\mathbf{b}+\mathbf{c}=0\) Then, \(\mathbf{a} \times \mathbf{b}=\mathbf{b} \times \mathbf{c}=\mathbf{c} \times \mathbf{a} \neq 0\) Now, if \(\mathbf{a}+x \mathbf{b}+y \mathbf{c}=0\) Let…
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