Equation of Plane: JEE Questions & Solutions

Let a point A lie between the parallel lines L1 and L2 such that its distances from L1 and L2 are 6 and 3 units, respectively. Then the…

Let the plane containing the line of intersection of the planes P1: x + ( + 4)y + z = 1 and P2: 2x + y + z = 2 pass through the points (0,…

Let the equation of the plane passing through the line x - 2y - z - 5 = 0 and x + y + 3z - 5 = 0, and parallel to the line x + y + 2z - 7 =…

Let the equation of the plane P containing the line x + 10 = 8 - y2 = z be ax + by + 3z = 2(a + b), and the distance of the plane P from…

The plane 2x - y + z = 4 intersects the line segment joining the points A(a, -2, 4) and B(2, b, -3) at the point C in the ratio 2:1, and…

Let a unit vector OP make angles,, with the positive directions of the coordinate axes OX, OY, OZ respectively, where ( 0, 2), and OP is…

1 < 2 are two values of such that the angle between the planes P1: r (3 i - 5 j + k) = 7 and P2: r ( i + j - 3 k) = 9 is ^-1 ( 2 65), then…

If the equation of the plane passing through the point (1, 1, 2) and perpendicular to the line x - 3y + 2z - 1 = 0, 4x - y + z = 0 is Ax +…

A vector v in the first octant is inclined to the x-axis at 60^, to the y-axis at 45^ and to the z-axis at an acute angle. If a plane…

If a plane passes through the points (-1, k, 0), (2, k, -1), (1, 1, 2) and is parallel to the line x-11 = 2y+12 = z+1-1, then the value of…

Let be the angle between the planes P1: r ( i + j + 2 k) = 9 and P2: r (2 i - j + k) = 15. Let L be the line that meets P2 at the point (4,…

Let P be the plane, passing through the point (1, -1, -5) and perpendicular to the line joining the points (4, 1, -3) and (2, 4, 3). Then…

Let the plane P: 8x + y + z + 12 = 0 be parallel to the line L: x+22 = y-33 = z+45. If the intercept of P on the y-axis is 1, then the…

The foot of perpendicular from the origin O to a plane P which meets the coordinate axes at the points A, B, C is (2, 4, 4). If the volume…

Let the image of the point P(2, -1, 3) in the plane x + 2y - z = 0 be Q. Then the distance of the plane 3x + 2y + z + 29 = 0 from the point…

Let the plane P pass through the intersection of the planes 2x + 3y - z = 2 and x + 2y + 3z = 6, and be perpendicular to the plane 2x + y -…

Let x + y + yz = 1 be the equation of a plane passing through the point (3, -2, 5) and perpendicular to the line joining the points (1, 2,…

If the equation of the plane passing through the line of intersection of the planes 2x - y + z = 3 and 4x - 3y + 5z + 9 = 0 and parallel to…

Let the image of the point P(1, 2, 3) in the plane 2x - y + z = 9 be Q. If the coordinates of the point R are (6, 10, 7), then the square…

A plane P contains the line of intersection of the plane r.( i+ j+ k) = 6 and r.(2 i+3 j+4 k) = -5. If P passes through the point (0, 2,…

Let the line L pass through the point (0, 1, 2), intersect the line x-12 = y-23 = z-34 and be parallel to the plane 2x + y - 3z = 4. Then…

If the equation of the plane containing the line x + 2y + 3z - 4 = 0, 2x + y - z + 5 = 0, and perpendicular to the plane r = ( i - j) + ( i…

Let 1, 2 be the values of for which the points (1,, 12) and (-2, 0, 1) are at equal distance from the plane 2x + 3y - 6z + 7 = 0. If 1 2,…

Let two vertices of a triangle ABC be (2, 4, 6) and (0,-2,-5), and its centroid be (2, 1,-1). If the image of the third vertex in the plane…

Let P be the point of intersection of the line x+33 = y+21 = 1-z2 and the plane x + y + z = 2. If the distance of the point P from the…

Let time 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(,,). Then ^2…

Let the line x1 = 6 - y2 = z + 85 intersect the lines x - 54 = y - 73 = z + 21 and x + 36 = 3 - y3 = z - 61 at the points A and B…

Let the foot of perpendicular from the point A(4, 3, 1) on the plane P: x - y + 2z + 3 = 0 be N. If B(5,,) is a point on plane P such that…

If equation of the plane that contains the point (-2,3,5) and is perpendicular to each of the planes 2x + 4y + 5z = 8 and 3x - 2y + 3z = 5,…

Let,, be the image of the point P(3, 3, 5) in the plane 2x + y - 3z = 6. Then + + is equal to:

Let P be the plane passing through the points (5, 3, 0), (13, 3, -2), and (1, 6, 2). For N, if the distances of the points A(3, 4,) and…

Let the line passing through the point P(2, -1, 2) and Q(5, 3, 4) meet the plane x - y + z = 4 at the point T. Then the distance of the…

Let the line: x = 1 - y-2 = z - 3, R meet the plane P: x + 2y + 3z = 4 at the point (,,). If the angle between the line and the plane P is…

Let the plane P: 4x - y + z = 10 be rotated by an angle 2 about its line of intersection with the plane x + y - z = 4. If is the distance…

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 (,, 67), then…

The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parallel to the line passing through (5,1,-7) and (1,-1,-1), also…

Let N be the foot of perpendicular from the point P(1, -2, 3) on the line passing through the points (4, 5, 8) and (1, -7, -5). Then the…

Let the foot of the 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(,,).…

Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line x+22= 3-y-4= z-75. Then the distance of the point…