PYQ Vault

Day 195: CBSE Class 12 Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Three Dimensional Geometry. Asked once: 2022 (same type asked 4 times)

    Electrical transmission wires which are laid down in winters are stretched tightly to accommodate expansion in summers. Two such wires lie along the following lines : l1:x+13=y−3−2=z+2−1l_1 : \frac{x + 1}{3} = \frac{y - 3}{-2} = \frac{z + 2}{-1} l2:x−1=y−73=z+7−2l_2 : \frac{x}{-1} = \frac{y - 7}{3} = \frac{z + 7}{-2} Based on the given information, answer the following questions :
    14 (i)
    Are the lines l1l_1 and l2l_2 coplanar ? Justify your answer.
    14 (ii)
    Find the point of intersection of the lines l1l_1 and l2l_2.

  2. Question 2

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    25
    Find the value of p, so that lines x−1−2=y−43p=z−34\frac{x-1}{-2} = \frac{y-4}{3p} = \frac{z-3}{4} and x−24p=y−52=1−z7\frac{x-2}{4p} = \frac{y-5}{2} = \frac{1-z}{7} are perpendicular to each other.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    23
    Find the direction cosines of the line whose Cartesian equations are 5x −- 3 = 15y + 7 = 3 −- 10z.

  4. Question 4

    Three Dimensional Geometry. Asked once: 2022 (same type asked 4 times)

    13
    Find the coordinates of the point where the line through (5,1,6)(5, 1, 6) and (3,4,1)(3, 4, 1) crosses the zx-plane.

  5. Question 5

    Vector Algebra. Asked once: 2022 (same type asked 4 times)

    7
    ABCD is a parallelogram such that AC→=i^+j^\overrightarrow{AC} = \hat{i} + \hat{j} and BD→=2i^+j^+k^\overrightarrow{BD} = 2\hat{i} + \hat{j} + \hat{k}. Find AB→\overrightarrow{AB} and AD→\overrightarrow{AD}. Also, find the area of the parallelogram ABCD.