If the line joining the points A(7, p, 2) and | vedclass

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(A) The direction ratios of the line $AB$ are $(q-7, -2-p, 5-2)$,which simplifies to $(q-7, -2-p, 3)$.The direction ratios of the line $CD$ are $(-6-2

Vedclass · Accepted Answer

$25$

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(A) The direction ratios of the line $AB$ are $(q-7, -2-p, 5-2)$,which simplifies to $(q-7, -2-p, 3)$.The direction ratios of the line $CD$ are $(-6-2, -15-(-3), 11-5)$,which simplifies to $(-8, -12, 6)$.Since the lines $AB$ and $CD$ are parallel,their direction ratios must be proportional:$\frac{q-7}{-8} = \frac{-2-p}{-12} = \frac{3}{6}$.Simplifying the ratio $\frac{3}{6}$,we get $\frac{1}{2}$.Equating $\frac{q-7}{-8} = \frac{1}{2}$:$q-7 = -4 \Rightarrow q = 3$.Equating $\frac{-2-p}{-12} = \frac{1}{2}$:$-2-p = -6 \Rightarrow p = 4$.Therefore,$p^2 + q^2 = 4^2 + 3^2 = 16 + 9 = 25$.

If the line joining the points $A(7, p, 2)$ and $B(q, -2, 5)$ is parallel to the line joining the points $C(2, -3, 5)$ and $D(-6, -15, 11)$,then the value of $p^2 + q^2$ is equal to

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