Find a unit vector perpendicular to each of the vector

If a unit vector makes angles and an acute angle θ with then find θ and hence, the components of .

Show that

Find λ and μ if

Given that What can you conclude about the vectors ?

Let the vectors be given as Then show that

If either then Is the converse true? Justify your answer with an example.

Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

Find the area of the parallelogram whose adjacent sides are determined by the vectors

Let the vectors be such that then is a unit vector, if the angle between is

Area of a rectangle having vertices A, B, C and D with position vectors respectively is