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Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry1 Mark
Question
The direction ratios of two mutually perpendicular lines are $1,2,3$ and $3,2, \lambda$. Then write the value of $\lambda$.
✓

Answer

For being perpendicular
$
\begin{array}{rlrl}
a_1 a_2+b_1 b_2+c_1 c_2 =0 \\
1 \times 3+2 \times 2+3 \times \lambda =0 \\
\Rightarrow 3+4+3 \lambda =0 \\
\therefore 3 \lambda =-7 \\
\Rightarrow \lambda =-\frac{7}{3} \quad \text { }
\end{array}
$

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