Three Dimensional Geometry: Class 12 Previous Year Questions

Three Dimensional Geometry questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Assertion (A) : A line can have direction cosines < 1, 1, 1 > 1 Reason (R) : cos  = 1 is possible for  = 0.
   Board 20261 markAssertion-Reason
2. (a) Find the shortest distance between the lines : x+1 y-1 z-9 and -3 x-3 y+15 z-9 -7 OR Find the image (b) of the pointä A(2, l, 2) in the line l := 4i + 2+ 2+ (i--k). Also, find the equation of line joining AA'. Find the foot of perpendicular from point A on…
   Board 20255 markslong answer
3. (a) Verify that lines given by = (1 - 2)i + (· - 2) + (3 - 22) and = (· + 1)i + (2· - 1) - (2· + 1)k are skew lines. Hence, find shortest distance between the lines. OR (b) During a cricket match, the position of the bowler, the wicket keeper W = 6i + 12§ and …
   Board 20253 marksshort answer
4. If the direction cosines of a line are 3 k, 3 k, 3 k, then the value of k is : (A) ± 1 (B) ± 3 (C) ± 3 (D) ± 3
   Board 20241 markMCQ
5. (a) Find the vector and the Cartesian equations of a line passing through the point (1, 2, 4) and parallel to the line joining the points A(3, 3, 5) and B(1, 0, 11). Hence, find the distance between the two lines. OR (b) Find the equations of the line passing …
   Board 20235 markslong answer
6. Page 4 of 7 10. (H$) {~ÝXþAm| (2, 1, 0), (3, 2, 2) Am¡a (1, 1, 7) go JwµOaZo dmbo g_Vb H$m g_rH$aU kmV H$s{OE & Bg g_Vb H$s _yb-{~ÝXþ go Xÿar ^r kmV H$s{OE & 3 AWdm (I) aoImAm| x = 2 1 y = 3 2 z VWm x + 1 = 2 2 y = 3 1 z Ho$ ~rM H$s Xÿar kmV H$s{OE & 3 4. A pa…
   Board 20221 markvery short
7. Find the equations of the lines through the origin which intersect the line 3 3 2 1 1 x y z     at an angle of 3 each. OR Find the equation of the line which intersect the lines 2 3 1 1 2 4 x y z      and 1 2 3 2 3 4 x y z      and passes throug…
   CBSE practice 2023-245 markslong answer
8. (A). Find the foot of the perpendicular drawn from the point (2,1,4) on the line 𝑥−2 = 2𝑦+3 4 = 2 −𝑧. Also find the equation of the line passing through this point and the point (2,1,4). 3 OR Q30 (B). Find the angle between the lines: 𝑥−1 2 = 𝑦−1 2 = 𝑧−2 1 and…
   Sample paper 2026-273 marksshort answer
9. i) Find the vector and cartesian equations of the straight line passing through the point (-5, 7, -4) and in the direction of (3, -2, 1). ii) Find the point where this straight line crosses the xy-plane. Show your work. OR 5 Given below are two lines L1 and L2…
   CBSE practice 2023-245 markslong answer
10. The direction ratios of the line 3x + 1 = 6y − 2 = 1 – z are (a) 3, 6, 1 (b) 3, 6, -1 (c) 2, 1, 6 (d) 2, 1, -6 ASSERTION-REASON BASED QUESTIONS The following questions consist of two statements – Assertion (A) and Reason (R). Answer these questions selecting t…
    CBSE practice 2023-241 markAssertion-Reason
11. The vector form of equations of two lines, l1 and l2 are: Show that l1 and l2 are skew lines.
    CBSE practice 2021-223 marksshort answer
12. L1 and L2 are two skew lines. 1 How many lines joining L1 and L2 can be drawn such that the line is perpendicular to both L1 and L2 ? (a) exactly one (b) exactly two (c) infinitely many (d) (there cannot be a line joining two skew lines such that it is perpend…
    CBSE practice 2023-241 markMCQ

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