WBJEE · Physics · Mathematics in Physics
Three vectors \(\mathbf{A}=a \mathbf{i}+\mathbf{j}+\mathbf{k} ; \mathbf{B}=\mathbf{i}+b \mathbf{j}+\mathbf{k}\)
and \(\mathbf{C}=\mathbf{i}+\mathbf{j}+c \mathbf{k}\) are mutually perpendicular (i, \(\mathbf{j}\) and \(\mathbf{k}\) are unit vectors along \(X, Y\) and \(Z\) axes respectively). The respective values of \(a\), \(b\) and \(c\) are
- A 0,0,0
- B \(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}\)
- C 1,-1,1
- D \(\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Three vectors are mutually perpendicular, so the scalar or dot product of two vectors will zero. So, \(\mathbf{A} \cdot \mathbf{B}=0, \mathbf{B} \mathbf{C}=0,\) So,…
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