RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 26. Scalar Triple Product

Subject: Maths - Class 12th

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Chapter Exercises

Exercise 26.1
Very short answer
MCQ

Exercise 26.1

1

Evaluate the following :
1

Evaluate the following :
2

Find when

and

2

Find when

and

3

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors:
3

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors:
3

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors:
3

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors:
4

Show that each of the following triads of vectors is coplanar :
4

Show that each of the following triads of vectors is coplanar :
4

Show that each of the following triads of vectors is coplanar :
5

Find the value of λ so that the following vectors are coplanar.
5

Find the value of λ so that the following vectors are coplanar.
5

Find the value of λ so that the following vectors are coplanar.
5

Find the value of λ so that the following vectors are coplanar.
6

Show that the four points having position vectors are not coplanar.
7

Show that the points A( – 1, 4, – 3), B(3, 2, – 5), C( – 3, 8, – 5) and D( – 3, 2, 1) are coplanar.
8

Show that four points whose position vectors are are coplanar.
9

Find the value of for which the four points with position vectors and are coplanar.
10

Prove that : -
11

and are the position vectors of points A, B and C respectively, prove that : is a vector perpendicular to the plane of triangle ABC.
12

Let and Then,

If and find which makes and coplanar.
12

Let and Then,

If and show that no value of can make and coplanar.
13

Find for which the points A(3, 2, 1), B(4, λ, 5), C(4, 2, – 2) and D(6, 5, – 1) are coplanar.
14

If four points A, B, C and D with position vectors and respectively are coplanar, then find the value of x.

Very short answer

1

Write the value of

2

Write the value of

3

Write the value of

4

Find the values of ‘a’ for which the vectors and are coplanar.
5

Find the volume of the parallelepiped with its edges represented by the vectors

6

If are non-collinear vectors, then find the value of

7

If the vectors (sec2 A) are coplanar, then find the value of cosec2A A + cosec2B + cosec2C.
8

For any two vectors of of magnitudes 3 and 4 respectively, write the value of

9

If then find the value of λ + μ.
10

If are non-coplanar vectors, then find the value of

11

Find , if and

MCQ

1

Mark the correct alternative in each of the following:

If lies in the plane of vectors and , then which of the following is correct?
2

Mark the correct alternative in each of the following:

The value of , where ,, is
3

Mark the correct alternative in each of the following:

If , , are three non-coplanar mutually perpendicular unit vectors, then is
4

Mark the correct alternative in each of the following:

If for some non-zero vector , then the value of , is
5

Mark the correct alternative in each of the following:

For any three vector the expression equals
6

Mark the correct alternative in each of the following:

If , , are non-coplanar vectors, then is
7

Mark the correct alternative in each of the following:

Let and be three non-zero vectors such that c⃗ is a unit vector perpendicular to both a⃗ and b⃗ . If the angle between a⃗ and b⃗ is, then is equal to
8

Mark the correct alternative in each of the following:

If and then the volume of the parallelepiped with conterminous edges , , is
9

Mark the correct alternative in each of the following:

If then


10

Mark the correct alternative in each of the following:
11

Mark the correct alternative in each of the following:

If the vectors and are coplanar, then m =
12

Mark the correct alternative in each of the following:

For non-zero vectors a⃗, b⃗ and c⃗ the relation holds good, if
13

Mark the correct alternative in each of the following:
14

Mark the correct alternative in each of the following:

If a⃗ ,b⃗,c⃗ are three non-coplanar vectors, then equal.
15

Mark the correct alternative in each of the following:

is equal to