The line joining the points (-2, 1, -8) and ( | vedclass

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Question

(A) The direction ratios of the line joining the points $P(-2, 1, -8)$ and $Q(a, b, c)$ are given by $(a - (-2), b - 1, c - (-8))$,which simplifies to

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$4, 3, -5$

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(A) The direction ratios of the line joining the points $P(-2, 1, -8)$ and $Q(a, b, c)$ are given by $(a - (-2), b - 1, c - (-8))$,which simplifies to $(a + 2, b - 1, c + 8)$.Since this line is parallel to the line with direction ratios $6, 2, 3$,their direction ratios must be proportional.Therefore,$\frac{a + 2}{6} = \frac{b - 1}{2} = \frac{c + 8}{3} = k$ for some constant $k$.If we take $k = 1$,we get $a + 2 = 6 \Rightarrow a = 4$,$b - 1 = 2 \Rightarrow b = 3$,and $c + 8 = 3 \Rightarrow c = -5$.Thus,the values are $a = 4, b = 3, c = -5$.

The line joining the points $(-2, 1, -8)$ and $(a, b, c)$ is parallel to the line whose direction ratios are $6, 2, 3$. The values of $a, b, c$ are

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