Find the unit vector in the direction of 3i + 4k.
Vectors
Original Khojo Papers practice question — not from a past board paper.
The scalar product gives the product of the magnitude of one vector and the projection of the other on it, and it is zero when the vectors are perpendicular. The vector product gives a vector perpendicular to both, whose magnitude is the area of the parallelogram they span, and it is zero when the vectors are parallel.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
The direction of the vector product is given by the right-hand rule.
From the same topic and chapter, at a similar level.
Find the unit vector in the direction of 3i + 4k.
Vectors
Find the area of the parallelogram whose adjacent sides are i + j and j + k.
Vectors
Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.
Vectors
For a = i + 2j + 3k and b = 4i + 5j + 6k, find a × b.
Vectors
If a = i + 2j + 3k and b = 4i + 5j + 6k, find a · b.
Vectors
If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.
Matrices