A line segment PQ has the length 63 and direc | vedclass

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(B) The direction ratios of the line segment $PQ$ are given as $(a, b, c) = (3, -2, 6)$.First,we calculate the magnitude of the direction vector: $\sq

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$-27, 18, -54$

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(B) The direction ratios of the line segment $PQ$ are given as $(a, b, c) = (3, -2, 6)$.First,we calculate the magnitude of the direction vector: $\sqrt{3^2 + (-2)^2 + 6^2} = \sqrt{9 + 4 + 36} = \sqrt{49} = 7$.The direction cosines $(l, m, n)$ are obtained by dividing the direction ratios by the magnitude: $l = \frac{3}{7}, m = \frac{-2}{7}, n = \frac{6}{7}$.The vector $\vec{PQ}$ has length $63$,so $\vec{PQ} = 63 	imes (l, m, n) = 63 	imes (\frac{3}{7}, \frac{-2}{7}, \frac{6}{7}) = (27, -18, 54)$.However,the problem states that the line makes an obtuse angle with the $X$-axis. This means the direction cosine $l$ must be negative.Therefore,we multiply the vector by $-1$: $\vec{PQ} = (-27, 18, -54)$.Thus,the correct option is $B$.

$A$ line segment $PQ$ has the length $63$ and direction ratios $(3, -2, 6)$. If this line makes an obtuse angle with the $X$-axis,then the components of the vector $\vec{PQ}$ are

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