JEE-MAIN SERIES Mathematics
Distance Of A Point From A Plane
16 previous year questions.
Volume: 16 Ques
Yield: Medium
High-Yield Trend
1
2025 1
2024 11
2023 1
2022 2
2019 Chapter Questions 16 MCQs
01
PYQ 2019
medium
mathematics ID: jee-main
The plane through the intersection of the planes and and parallel to y-axis also passes through the point :
1
(-3, 0, -1)
2
(3, 3, -1)
3
(3, 2, 1)
4
(-3, 1, 1)
02
PYQ 2019
medium
mathematics ID: jee-main
The plane which bisects the line segment joining the points (-3,-3,4) and (3,7,6) at right angles, passes through which one of the following points ?
1
(4, -1,7)
2
(4,1,-2)
3
(-2,3,5)
4
(2,1,3)
03
PYQ 2022
medium
mathematics ID: jee-main
Let d be the distance between the foot of perpendiculars of the point P(1, 2, –1) and Q(2, –1, 3) on the plane –x + y + z = 1. Then d2 is equal to ____.
04
PYQ 2023
medium
mathematics ID: jee-main
Let the equation of the plane P containing the line be and the distance of the plane P from the point (1, 27, 7) be c. Then a2+b2+c2 is equal to ____________.
05
PYQ 2023
medium
mathematics ID: jee-main
Let P be the plane passing through the line and the point (2, 4, –3). If the image of the point (-1, 3, 4) in the plane P is (\alpha , \beta , \gamma ) then \alpha + \beta + \gamma is equal to
1
9
2
10
3
11
4
12
06
PYQ 2023
easy
mathematics ID: jee-main
For and , let the angle between the plane and the line be . If the distance of the point from the plane is , then is equal to:
1
25
2
32
3
48
4
85
07
PYQ 2023
medium
mathematics ID: jee-main
Let P₁ be the plane 3x-y-7z = 11 and P₂ be the plane passing through the points (2,-1,0), (2,0,-1), and (5,1,1). If the foot of the perpendicular drawn from the point (7,4,-1) on the line of intersection of the planes P₁ and P₂ is (α, β, γ), then a + ẞ+ y is equal to
08
PYQ 2023
medium
mathematics ID: jee-main
Let P be the point of intersection of the line and the plane x + y + z = 2. If the distance of the point P from the plane 3x – 4y + 12z = 32 is q, then q and 2q are the roots of the equation
1
2
3
4
09
PYQ 2023
medium
mathematics ID: jee-main
Let the foot of perpendicular of the point P(3, -2, -9) on the plane passing through the points (-1, -2, -3), (9, 3, 4), (9, -2, 1) be Q(α, β, γ). Then the distance of Q from the origin is
1
√35
2
√38
3
√49
4
√52
10
PYQ 2023
medium
mathematics ID: jee-main
Let S be the set of all values of \lambda , for which the shortest distance between the lines x-\lambda /0 =y-3/4 = z+6/1 and x+\lambda /3 = y/-4 = z-6/0 is 13. Then 8 |
1
302
2
304
3
306
4
308
11
PYQ 2023
easy
mathematics ID: jee-main
Let be the values of for which the points and are at equal distance from the plane . If , then the distance of the point from the line is:
12
PYQ 2023
medium
mathematics ID: jee-main
Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α2 + β2 + γ2) is equal to
1
62
2
65
3
70
4
76
13
PYQ 2023
medium
mathematics ID: jee-main
Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line . Then the distance of the point
A(8, -1, -19) from the plane P measured parallel to the line is equal to ___________.
A(8, -1, -19) from the plane P measured parallel to the line is equal to ___________.
14
PYQ 2023
medium
mathematics ID: jee-main
Let the plane x+3y–2z+6=0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is then 98(α + β)2 is equal to___.
15
PYQ 2024
medium
mathematics ID: jee-main
An equation of a plane parallel to the plane and at a unit distance from the origin is?
16
PYQ 2025
medium
mathematics ID: jee-main
The square of the distance of the point from the line in the direction of the vector is:
1
2
3
4