A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the centre of the sphere OABC, O being the origin, is
The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7 and perpendicular to the piane x - 5y + 3z = 5 is given by :
x + 2y + 3z - 6 = 0
x + 2y + 3z + 6 = 0
x + 4y + 5z - 8 = 0
3x + 4y + 5z + 8 = 0
A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z = 1 and the point(1, 0, 1). What are the direction ratios of the line of intersection of the.given planes ?
(2, - 5, - 3)
(1, - 5, - 3)
(2, 5, 3)
(1, 3, 5)
A.
(2, - 5, - 3)
A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z = 1 and the point(1, 0, 1). What is the equation of the plane P ?
2x + 5y - 2 = 0
5x + 2y - 5 = 0
x + y - 2 = 0
2x - y - 2z = 0
A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z = 1 and the point(1, 0, 1). If the plane P touches the sphere x2 + y + z2 = r, then what is r equal to ?
1
Let Q be the image of the point P ( - 2, 1, - 5) in the plane 3x - 2y + 2z + 1 = 0.
Consider the following :
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Let Q be the image of the point P ( - 2, 1, - 5) in the plane 3x - 2y + 2z + 1 = 0.
Consider the following :
Which of the above statements is/are correct ?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
A line L passes through the point P(5, - 6, 7) and is parallel to the planes x + y + z = 1 and 2x - y - 2z = 3.
What are the direction ratios of the line of intersection of the given planes ?
< 1, 4, 3 >
< - 1, - 4, 3 >
< 1, - 4, 3 >
< 1, - 4, - 3 >
A line L passes through the point P(5, - 6, 7) and is parallel to the planes x + y + z = 1 and 2x - y - 2z = 3.
What is the equation of the line ?
A straight line passes through the point (1, 1, 1) makes an angle 60o with the positive direction of z-axis, and the cosine of the angles made by it with the positive directions of the y-axis and the x-axis are in the ration . What is the acute angle between the two possible positions of the line ?