GeeksforGeeks App
Open App
Browser
Continue

## Related Articles

• RD Sharma Class 12 Solutions for Maths

# Class 12 RD Sharma Solutions – Chapter 25 Vector or Cross Product – Exercise 25.1 | Set 1

Solution:

Given, and  .

=>

=>

=>

=>

=>

Now,

=>

=>

=> = √91

Solution:

Given,  and

=>

=>

=>

=>

=>

Now,

=>

=>

=>

Solution:

Given,  and

=>

=>

=>

=>

=>

Now,

=>

=>

=> = √6

### Question 3(i). Find a unit vector perpendicular to both the vectors  and

Solution:

Given  and

A vector perpendicular to 2 vectors is given by

=>

=>

=>

=>

=>

Unit vector is given by

=>  =

=>

=> = 3

=> Unit vector is,

=>

### Question 3(ii). Find a unit vector perpendicular to the plane containing the vectors  and  .

Solution:

Given, and

A vector perpendicular to 2 vectors is given by

=>

=>

=>

=>

=>

Unit vector is given by

=>

=>

=>

=> Unit vector is,

=>

Solution:

Given

=>

=>

=>

=>

=>

Unit vector is,

=>

=>

=> = √74

Solution:

Given, and

=>

=>

=>

=>

=>

=>

=>

=>

Now,

=>

=>

=>

Solution:

Given,  and

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

### Question 7(i). Find a vector of magnitude 49, which is perpendicular to both the vectors  and

Solution:

Given,  and

A vector perpendicular to 2 vectors is given by

=> =

=>  =

=>  =

=>  =

=>

Magnitude of vector is given by,

=>

=>

=>

=>

=> Vector is,

### Question 7(ii). Find the vector whose length is 3 and which is perpendicular to the vector and

Solution:

Given,  and

A vector perpendicular to 2 vectors is given by

=>

=>

=>

=>

=>

Magnitude of vector is given by,

=>

=>

=>

=> = 27

=> Unit vector is,

=>

=>

Required vector is,

=>

### Question 8(i). Find the parallelogram determined by the vectors:  and

Solution:

Given that, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area = 6 square units.

### Question 8(ii). Find the parallelogram determined by the vectors:  and .

Solution:

Given that, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus, the area of parallelogram is,

=>

=>

=> Area =

### Question 8(iii). Find the area of the parallelogram determined by the vectors:  and

Solution:

Given that, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area =

### Question 8(iv). Find the area of the parallelogram determined by the vectors:  and

Solution:

Given that,  and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area =

### Question 9(i). Find the area of the parallelogram whose diagonals are: and

Solution:

Given, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area = 15/2 = 7.5 square units

### Question 9(ii). Find the area of the parallelogram whose diagonals are:  and

Solution:

Given, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area =

### Question 9(iii). Find the area of the parallelogram whose diagonals are:  and

Solution:

Given, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area =

### Question 9(iv). Find the area of the parallelogram whose diagonals are:  and

Solution:

Given, and

=> Area of the parallelogram is

=>

=>

=>

=>

=>

Thus the area of parallelogram is,

=>

=>

=> Area =

=> Area = 24.5

### Question 10. If  ,  and , compute  and  and verify these are not equal.

Solution:

Given and

=>

=>

=>

=>

=>

=>  =

=>  =

=>

=>

=>

=>

=>

=>

=>

=>

=>

=> is not equal to

=> Hence verified.

### Question 11. If ,  and , find

Solution:

We know that,

=>

=>

We know that  is 1, as  is a unit vector

=>

=>

=>

Also,

=>

And

=>

=>

=>

=>

=>

=>

### Question 12. Given , , , , , being a right-handed orthogonal system of unit vectors in space, show that ,  and  is also another system.

Solution:

To show that  and  is a right-handed orthogonal system of unit vectors, we need to prove:

(1)

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

=>

(2)

=>

=>

=>

=>

=>

(3)

=>

=>

=>

=>

=>

(4)

=>

=>

=>

=>

=>

Hence proved.

My Personal Notes arrow_drop_up
Related Tutorials