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AP EAMCET · Maths · Vector Algebra

If \(\mathbf{a}\) and \(\mathbf{b}\) are two unit vectors such that \(\mathbf{c}=(\mathbf{a} \times \mathbf{c})+\mathbf{b}\), then the maximum value of \([\mathbf{a} \mathbf{b c}]\) is

  1. A 1
  2. B \(\frac{1}{2}\)
  3. C \(\frac{3}{2}\)
  4. D 2
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \mathbf{c}=(\mathbf{a} \times \mathbf{c})+\mathbf{b} \\ & \Rightarrow \quad|\mathbf{c}|^2=|\mathbf{a}+\mathbf{c}|^2+|\mathbf{b}|^2+2(\mathbf{a} \times \mathbf{c}) \cdot \mathbf{b} \\ & \Rightarrow \quad 2[\mathbf{a b c}]=|\mathbf{a} \times…