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Let $P = (1, 2, 0), Q = (4, 0, - 2)$ are any two points in the space. Suppose that $d_{1}, d_{2}$ are the projections of $P Q$ on the $x -$ axis, $y z - p l a n e$ respectively, then $|{d_{1}}^{2} - {d_{2}}^{2}|$

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Correct option is A

The projection of PQ on x- axis is x2−x1Hence, the projection of PQon x-axis is d1=3The projection of PQ on yz-plane is y2−y12+z2−z12Hence, the projection of PQ on xy- plane is 0−22+−2−02=8=d2Therefore, d12−d22=9−8=1

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2023 | www.infinitylearn.com

Let P=1,2,0 , Q=4,0,−2 are any two points in the space. Suppose that d1,d2 are the projections of PQ on the x-axis, yz-plane respectively, then d12-d22

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Let $P = (1, 2, 0), Q = (4, 0, - 2)$ are any two points in the space. Suppose that $d_{1}, d_{2}$ are the projections of $P Q$ on the $x -$ axis, $y z - p l a n e$ respectively, then $|{d_{1}}^{2} - {d_{2}}^{2}|$