jee_main_2026_24_january_morning - Three Dimensional Geometry Topics

Master these core formulas and structures to solve almost any past paper question.

Sample Questions in this Chapter

QUESTION #3 Intersection of Lines and Distances
Let the lines L_1: vecr = hati + 2hatj + 3hatk + lambda(2hati + 3hatj + 4hatk), lambda in mathbbR and L_2: vecr = (4hati + hatj) + mu(5hati + 2hatj + hatk), mu in mathbbR, intersect at the point R. Let P and Q be the points lying on lines L_1 and L_2, respectively, such that |overrightarrowPR| = sqrt29 and |overrightarrowPQ| = sqrtfrac473. If the point P lies in the first octant, then 27(QR)^2 is equal to
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QUESTION #22 Lines and Parallelograms
Let a line L passing through the point P(1, 1, 1) be perpendicular to the lines fracx - 44 = fracy - 11 = fracz - 11 and fracx - 171 = fracy - 711 = fracz0. Let the line L intersect the yz-plane at the point Q. Another line parallel to L and passing through the point S(1, 0, -1) intersects the yz-plane at the point R. Then the square of the area of the parallelogram PQRS is equal to
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