AP EAMCET · Maths · Vector Algebra
\(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-coplanar vectors. If \(\begin{aligned} & \mathbf{a}+3 \mathbf{b}+4 \mathbf{c}=x(\mathbf{a}-2 \mathbf{b}+3 \mathbf{c})+y(\mathbf{a}+5 \mathbf{b}-2 \mathbf{c}) \\ & +z(6 \mathbf{a}+14 \mathbf{b}+4 \mathbf{c}), \text { then } x+y+z=\end{aligned}\)
- A \(-5\)
- B \(-4\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(-4\)
Step-by-step Solution
Detailed explanation
\(\mathbf{a}+3 \mathbf{b}+4 \mathbf{c}=\mathbf{a}(x+y+6 z)+\mathbf{b}(-2 x+5 y+14 z)\) \(+c(3 x-2 y+4 z)\) (because \(a, b\) and \(c\) are non-coplanar vectors) Comparing both sides, \(x+y+6 z=1\) ...(i) \(-2 x+5 y+14 z=3\) ...(ii) \(3 x-2 y+4 z=4\) ...(iii) By solving Eqs. (i),…
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