Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let P_1 be the plane 3x-y-7z=11 and P_2 be the plane passing through the points (2, –1, 0), (2, 0, –1), and (5, 1, 1). If the...
- If the equation of the plane containing the line x + 2y + 3z – 4 = 0 = 2x + y – z + 5 and perpendicular to the plane r =( i - j...
- Let _1, _2 be the values of for which the points ( 5 2 ,1, ) and (–2, 0, 1) are at equal distance from the plane 2x + 3y – 6z + 7...
- 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), C(0, 5, 1) be Q( , , )....
- Let the line x 1 = 6-y 2 = z+8 5 intersect the lines x-5 4 = y-7 3 = z+2 1 and x+3 6 = 3-y 3 = z-6 1 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, , ), , Z is a point on...
- 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...
- Let P be the point of intersection of the line x+3 3 = y+2 1 = 1-z 2 and the plane x + y + z = 2. If the distance of the point P...
- 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,...
- Let the line passing through the points P(2, –1, 2) and Q(5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance...
- Let the line l: x = 1-y -2 = z-3 , R meet the plane P : x + 2y + 3z = 4 at the point ( , , ). if the angle between the line l and...
- If the equation of the plane that contains the point (–2, 3, 5) and is perpendicular to each of the planes 2x + 4y + 5z = 8 and...
- Let a line l pass through the origin and be perpendicular to the lines l_1: r =( i -11 j -7 k )+ ( i +2 j +3 k ), R and l_2: r...
- 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...
- 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,...
- The line, that is coplanar to the line x+3 -3 = y-1 1 = z-5 5 is :
- 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)....
- Let the equation of plane passing through the line of intersection of the planes x + 2y + az = 2 and x – y + z = 3 be 5x – 11y +...
- The distance of the point (–1, 2, 3) from the plane r .( i -2 j +3 k )=10 parallel to the line of the shortest distance between...
- Let the image of the point ( 5 3 , 5 3 , 8 3 ) in the plane x – 2y + z – 2 = 0 be P. If the distance of the point Q(6, –2, ), >...
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