If and, find.

If and find the value of

If find the magnitude of

Find a unit vector perpendicular to both the vectors and

Find a unit vector perpendicular to the plane containing the vectors and

Find the magnitude of vector

If and then find

If and find

Find a vector of magnitude 49, which is perpendicular to both the vectors and

Find the vector whose length is 3 and which is perpendicular to the vector and

Find the area of the parallelogram determined by the vectors :

and

Find the area of the parallelogram determined by the vectors :

and

Find the area of the parallelogram determined by the vectors :

and

Find the area of the parallelogram determined by the vectors :

and

Find the area of the parallelogram whose diagonals are :

and

Find the area of the parallelogram whose diagonals are :

and

Find the area of the parallelogram whose diagonals are :

and

Find the area of the parallelogram whose diagonals are :

and

If and compute and and verify that these are not equal.

If and find

Given being a right handed orthogonal system of unit vectors in space, show that is also another system.

If and then find

Find the angle between two vectors and if

If, then show that, where m is any scalar.

If and find the angle between and

What inference can you draw if and

If are three unit vectors such that Show that form an orthonormal right handed triad of unit vectors.

Find a unit vector perpendicular to the plane ABC, where the coordinates of A, B and C are A(3, –1, 2), B(1, –1, –3) and C(4, –3, 1).

If a, b, c are the lengths of sides, BC, CA and AB of a triangle ABC, prove that and deduce that

If and then find Verify that and are perpendicular to each other.

If and are unit vectors forming an angle of 30^o, find the area of the parallelogram having and as its diagonals.

For any two vectors and prove that

Define and prove that where θ is the angle between and

If and find

Find the area of the triangle formed by O, A, B when

Let and Find a vector which is perpendicular to both and and

Find a unit vector perpendicular to each of the vectors and where and

Using vectors, find the area of the triangle with vertices A(2, 3, 5), B(3, 5, 8) and C(2, 7, 8).

If are three vectors, find the area of the parallelogram having diagonals and

The two adjacent sides of a parallelogram are and Find the unit vector parallel to one of its diagonals. Also, find its area.

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

If and then verify that

Using vectors, find the area of the triangle with vertices

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

Using vectors, find the area of the triangle with vertices

A(1, 2, 3), B(2, –1, 4) and C(4, 5, –1)

Find all vectors of magnitude that are perpendicular to the plane of and

If and then write the value of

Define vector product of two vectors.

Write the value

Write the value of

Write the value of .

Write the expression for the area of the parallelogram having and as its diagonals.

For any two vectors and write the value of in terms of their magnitudes.

If and are two vectors of magnitudes 3 and respectively such that is a unit vector. Write the angle between and .

If and , and .

For any two vectors and , find .

If and are two vectors such that and , find the angle between.

For any three vectors and write the value of

For any two vectors and , find .

Write the value of .

If and , then find .

Write a unit vector perpendicular to and.

If , then write the value of .

If and are unit vectors such that is also a unit vector, find the angle between and .

If and are two vectors such that , write the angle between and .

If and are unit vectors, then write the value of .

If is a unit vector such that , find .

If is a unit vector perpendicular to the vectors and , write another unit vector perpendicular to and.

Find the angle between two vectors and , with magnitudes 1 and 2 respectively and when .

Vectors and are such that and is a unit vector. Write the angle between and .

Find λ, if .

Write the value of the area of the parallelogram determined by the vectors and .

Write the value of .

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

Write the number of vectors of unit length perpendicular to both the vectors and .

Write the angle between the vectors and .

Mark the correct alternative in each of the following:

Mark the correct alternative in each of the following:

If and , then

Mark the correct alternative in each of the following:

The vector is to be written as sum of a vector parallel to and a vector perpendicular to . Then

Mark the correct alternative in each of the following:

The unit vector perpendicular to the plane passing through points and is

Mark the correct alternative in each of the following:

If represent the diagonals of a rhombus, then

Mark the correct alternative in each of the following:

Vectors and are inclined at angle θ = 120°. If , then is equal to

Mark the correct alternative in each of the following:

If and , then a unit vector normal to the vectors and is

Mark the correct alternative in each of the following:

A unit vector perpendicular to both and is

Mark the correct alternative in each of the following:

If and , then is

Mark the correct alternative in each of the following:

If are unit vectors, then

Mark the correct alternative in each of the following:

If θ is the angle between the vectors and , then sin θ =

Mark the correct alternative in each of the following:

If , then

Mark the correct alternative in each of the following:

The value of is

Mark the correct alternative in each of the following:

The value of , is

Mark the correct alternative in each of the following:

If θ is the angle between any two vectors and , then when θ is equal to