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Find and , when

and

Find λ if .

If and , find .

Verify that (i) and are perpendicular to each other

and (ii) and are perpendicular to each other.

Find the value of:

i. ii. iii.

Find the unit vectors perpendicular to both and when

Find the unit vectors perpendicular to the plane of the vectors

Find a vector of magnitude 6 which is perpendicular to both the vectors

and .

Find a vector of magnitude 5 units, perpendicular to each of the vectors

and, where and

Find an angle between two vectors and with magnitudes 1 and 2 respectively and .

If , and , find a vector which is perpendicular to both and and for which .

Prove that , where θ is the angle between and .

Write the value of p for which and are parallel vectors.

Verify that , when

, and

, and .

Find the area of the parallelogram whose adjacent sides are represented by the vectors:

Find the area of the parallelogram whose diagonal are represented by the vectors

Find the area of the triangle whose two adjacent sides are determined by the vectors

Using vectors, find the area of ΔABC whose vertices are

A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5)

A(1, 2, 3), B(2, −1, 4) and C(4, 5, Δ1) ((considering Δ1 as 1 ))

A(3, −1, 2), B(1, −1, −3) and C(4, −3, 1)

A(1, −1, 2), B(2, 1, −1) and C(3, −1, 2).

Using vector method, show that the given points A, B, C are collinear:

A(3, −5, 1), B(−1, 0, 8) and C(7, −10, −6)

A(6, −7, −1), B(2, −3, 1) and C(4, −5, 0).

Show that the point A, B, C with position vectors , and respectively are collinear.

Show that the points having position vectors are collinear, whatever be .

Show that the points having position vector , and are collinear, whatever be .

Find a unit vector perpendicular to the plane ABC, where the points A, B, C, are , and respectively.

If and then find .

If , and , find .

If , and , find the angle between and .