AP EAMCET · Maths · Vector Algebra
\((\mathbf{a}+\mathbf{b}) \cdot(\mathbf{b}+\mathbf{c}) \times(\mathbf{a}+\mathbf{b}+\mathbf{c})\) is equal to
- A \(0\)
- B \(-[\mathbf{a} \mathbf{b} \mathbf{c}]\)
- C \(2[\mathbf{a} \mathbf{b} \mathbf{c}]\)
- D \(\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}]\end{array}\right.\)
Answer & Solution
Correct Answer
(D) \(\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}]\end{array}\right.\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (a+b) \cdot(b+c) \times(a+b+c) \\ & =(a+b) \cdot(b \times a+0+b \times c+c \times a+c \times b+0) \\ & =(a+b) \cdot(b \times a+c \times a) \\ & =a(b \times a)+a(c \times a)+b(b \times a)+b \cdot(c+a) \\ & =0+0+0+[b c a]=[a b c]\end{aligned}\)
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