Define direction cosines and state the relation they satisfy.
Three-Dimensional Geometry
Original Khojo Papers practice question — not from a past board paper.
sin−1(4/√18), about 70.5°
No citable source has been recorded for this record. Treat it as practice material, not as fact.
The angle between a line and a plane is sin−1 of the modulus of the cosine of the angle between the line and the normal: sin θ = |1 + 1 + 2| ÷ (√6 × √3) = 4/√18.
From the same topic and chapter, at a similar level.
Define direction cosines and state the relation they satisfy.
Three-Dimensional Geometry
Find the equation of the plane passing through (1, 2, 3) with normal vector 2i − j + 3k.
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