PYQ Vault
EbooksTutor

Line parallel to a plane: find the unknown (direction perpendicular to the normal)

This type of question, asked 4 times: 3 May 2023 S1, 11 May 2023 S2, 15 May 2023 S1, 19 Apr 2026 S2. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    3 May 2023 S1

    146
    Let P(2,3,6)P(2,3,6) be a point in space and Q be a point on the line r⃗=(i^−j^+2k^)+μ(−3i^+j^+5k^)\vec{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu(-3\hat{i}+\hat{j}+5\hat{k}). Then the value of μ\mu for which vector PQ is parallel to the plane x−4y+4z=1x-4y+4z=1 is

    Tap an option to check your answer.

  2. Question 2

    11 May 2023 S2

    145
    Let P(3,2,6)P(3,2,6) be a point in space and Q be a point on the line r⃗=i^−j^+2k^+μ(−3i^+j^+5k^)\vec{r}=\hat{i}-\hat{j}+2\hat{k}+\mu(-3\hat{i}+\hat{j}+5\hat{k}). Then the value of μ\mu for which the vector PQ→\overrightarrow{PQ} is parallel to the plane x−4y+3z=1x-4y+3z=1 is

    Tap an option to check your answer.

  3. Question 3

    15 May 2023 S1

    138
    Let P(2,1,5) be a point in space and Q be a point on the line r⃗=(i^−j^+2k^)+μ(−3i^+j^+5k^)\vec{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu(-3\hat{i}+\hat{j}+5\hat{k}). Then the value of μ\mu for which the vector PQ is parallel to the plane 3x−y+4z=13x-y+4z=1 is

    Tap an option to check your answer.

  4. Question 4

    19 Apr 2026 S2

    94
    Let r⃗⋅(3i^−2j^+7k^)=32\vec{r}\cdot(3\hat{i} - 2\hat{j} + 7\hat{k}) = 32 is the equation of a plane and the line having direction ratios (5,b,3)(5, b, 3) is parallel to the plane, then the value of b is...

    Tap an option to check your answer.