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AP EAMCET · Maths · Vector Algebra

If \(\mathbf{a}\) makes an acute angle with \(\mathbf{b}, \mathbf{r} \cdot \mathbf{a}=0\) and \(\mathbf{r} \times \mathbf{b}=\mathbf{c} \times \mathbf{b}\), then \(\mathbf{r}=\)

  1. A \(\mathbf{a} \times \mathbf{c}-\mathbf{b}\)
  2. B \(c \times a\)
  3. C \(c-\left(\frac{c \cdot a}{b \cdot a}\right) b\)
  4. D \(c+\left(\frac{c \cdot a}{b \cdot a}\right) b\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(c-\left(\frac{c \cdot a}{b \cdot a}\right) b\)

Step-by-step Solution

Detailed explanation

Given, and \[ \begin{aligned} \mathbf{r} \cdot \mathbf{a} & =0 \\ \mathbf{r} \times \mathbf{b} & =\mathbf{c} \times \mathbf{b} \end{aligned} \] So, \[ \mathbf{r} \times \mathbf{b}=\mathbf{c} \times \mathbf{b} \]…