If the coordinates of the points P and Q are | vedclass

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(B) The coordinates of $O$ are $(0, 0, 0)$,$P$ are $(1, -2, 1)$,and $Q$ are $(2, 3, 4)$.The direction ratios of line $OP$ are $(1-0, -2-0, 1-0) = (1,

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$OP \perp OQ$

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(B) The coordinates of $O$ are $(0, 0, 0)$,$P$ are $(1, -2, 1)$,and $Q$ are $(2, 3, 4)$.The direction ratios of line $OP$ are $(1-0, -2-0, 1-0) = (1, -2, 1)$.The direction ratios of line $OQ$ are $(2-0, 3-0, 4-0) = (2, 3, 4)$.Two lines with direction ratios $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ are perpendicular if $a_1a_2 + b_1b_2 + c_1c_2 = 0$.Calculating the dot product: $(1 	imes 2) + (-2 	imes 3) + (1 	imes 4) = 2 - 6 + 4 = 0$.Since the dot product is $0$,the lines $OP$ and $OQ$ are perpendicular,i.e.,$OP \perp OQ$.

If the coordinates of the points $P$ and $Q$ are $(1, -2, 1)$ and $(2, 3, 4)$ respectively,and $O$ is the origin $(0, 0, 0)$,then which of the following is true?

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