Find the equation of the plane passing through (1, 2, 3) with normal vector 2i − j + 3k.
Three-Dimensional Geometry
Original Khojo Papers practice question — not from a past board paper.
The direction cosines of a line are the cosines of the angles it makes with the positive directions of the three coordinate axes, usually written l, m and n. They satisfy l2 + m2 + n2 = 1.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Direction ratios are any numbers proportional to the direction cosines.
From the same topic and chapter, at a similar level.
Find the equation of the plane passing through (1, 2, 3) with normal vector 2i − j + 3k.
Three-Dimensional Geometry
Find the angle between the line with direction ratios 1, 1, 2 and the plane x + y + z = 5.
Three-Dimensional Geometry
Find the distance of the point (1, 2, 3) from the plane 2x − y + 2z − 9 = 0.
Three-Dimensional Geometry
Find the angle between the planes 2x + y − 2z = 5 and 3x − 6y − 2z = 7.
Three-Dimensional Geometry
If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.
Matrices
Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.
Vectors