Question

Three vectors \(\vec{A}=a \vec{i}+\vec{j}+k ; B=\vec{i}+b \vec{j}+k\) and \(\vec{C}=\vec{i}+j+c \vec{k}\) are mutually perpendicular \((\vec{i}, \vec{j}\) and \(\vec{k}\) are unit vectors along \(X, Y\) and \(Z\) axis 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 1

\begin{aligned}
&a+b+1=0 \\
&1+b+c=0 \\
&a+1+c=0 \\
&2(a+b+c)+3=0 \\
&a+b+c=-\frac{3}{2} \\
&\Rightarrow-1+c=\frac{-3}{2} \\
&c=-0.5
\end{aligned}

Answer 2

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Answer 3

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