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Prove that

i.

ii.

Find when

i. and ..

ii. and

iii. and

Find the volume of the parallelepiped whose conterminous edges are represented by the vectors

iii.

iv.

Show that the vectors are coplanar, when

i. and

Find the value of λ for which the vectors are coplanar, when

If and find and interpret the result.

The volume of the parallelepiped whose edges are and is 546 cubic units. Find the value of λ.

Show that the vectors and are parallel to the same plane.

{HINT: Show that }

If the vectors and be coplanar, show that c^{2} = ab.

Show that the four points with position vectors and are coplanar.

Find the value of λ for which the four points with position vectors and are coplanar.

Ans. λ = 3

Using vector method, show that the points A(4, 5, 1), B(0, -1, -1), C(3, 9, 4) andD(-4, 4, 4) are coplanar.

Find the value of λ for which the points A(3, 2, 1), B(4, λ, 5), C(4, 2, -2) and D(6, 5, -1) are coplanar.

Ans. λ = 5

If and are two equal vectors the x + y + z = ?

Write a unit vector in the direction of the sum of the vectors and

Write the value of λ so that the vectors and are perpendicular to each other.

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

Find the value of λ when the projection of on is 4 units.

If and are perpendicular vectors such that and find the value of

If is a unit vector such that find

Find the sum of the vectors and

Write the projection of the vector along the vector

Write the projection of the vector on the vector

Find when and

Find a vector in the direction of which has magnitude 21 units.

If and are such that is perpendicular to then find the value of λ.

Write the vector of magnitude 15 units in the direction of vector

If and find a vector of magnitude 6 units which is parallel to the vector

Write the angle between two vectors and with magnitudes and 2 respectively having

If and then find

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

What conclusion can you draw about vectors and when and

Find the value of λ when the vectors and are parallel.

Write the value of

Find the volume of the parallelepiped whose edges are represented by the vectors and

If and then prove that and are coplanar.

If and are such that then find the values of λ and μ.

If θ is the angle between and and then what is the value of θ?

When does hold?

Find the direction cosines of a vector which is equally inclined to the x - axis, y - axis and z - axis.

If P(1, 5, 4) and Q(4, 1, - 2) be the position vectors of two points P and Q, find the direction ratios of

Find the direction cosines of the vector .

If and are unit vectors such that is a unit vector, what is the angle between and ?

Write the vector of magnitude 15 units in the direction of the vector

Mark (√) against the correct answer in each of the following:

A unit vector in the direction of the vector is

The direction cosines of the vector are

If A(1, 2, -3) and B(-1, -2, 1) are the end points of a vector then the direction cosines of are

If a vector makes angle α, β and γ with the x-axis, y-axis and z-axis respectively then the value of (sin^{2}α + sin^{2}β + sin^{2}γ) is

The vector is a

What is the angle which the vector makes with the z-axis?

f and are vectors such that and then the angle between and is

If and are two vectors such that and then the angle between and is

The angle between the vectors and is

If and then the angle between and is

If and be such that then λ = ?

What is the projection of on ?

If then

If and are mutually perpendicular unit vectors then

If the vectors and are perpendicular to each other then λ = ?

If θ is the angle between two unit vectors and then

If and then

Two adjacent sides of a || gm are represented by the vectors and The area of the || gm is

The diagonals of a || gm are represented by the vectors and The area of the || gm is

Two adjacent sides of a triangle are represented by the vectors and The area of the triangle is

The unit vector normal to the plane containing and is

If and are unit vectors such that then

If and be the coterminous edges of a parallelepiped then its volume is

If the volume of a parallelepiped having and as conterminous edges, is 216 cubic units then the value of λ is

It is given that the vectors and are coplanar. Then, the value of λ is

Which of the following is meaningless?

For any three vectors the value of is

Mark (√) against the correct answer in the following:

if and are vectors such that and then the angle between and is