TS EAMCET · Maths · Vector Algebra
It is given that \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are vectors of lengths 6,8 , 10 respectively. If a is perpendicular to \((\mathbf{b}+\mathbf{c}), \mathbf{b}\) is perpendicular (c+a); and \(\mathbf{c}\) is perpendicular to \((\mathbf{a}+\mathbf{b})\), then the length of the vector of \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is
- A \(6 \sqrt{2}\)
- B \(12 \sqrt{2}\)
- C \(5 \sqrt{2}\)
- D \(10 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(10 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & |\mathbf{a}|=6,|\mathbf{b}|=8, \mid \mathbf{c}=10, \mathbf{a} \perp(\mathbf{b}+\mathbf{c}), \\ & \mathbf{b} \perp(\mathbf{c}+\mathbf{a}) \text { and } \mathbf{c} \perp(\mathbf{a}+\mathbf{b}) \end{aligned}\) From the given condition, we have…
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