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Let the vectors be given as Then show that
Given that
and
Solving for left hand side,
First, we calculate
(Property of determinant)
Which is equal to R.H.S.
Hence proved.
Find if
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 ?
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