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**Download NCERT solutions for Vector Algebra as PDF.**

## NCERT Solutions class 12 Maths Vector Algebra

**Vector Algebra**

Exercise 10.4

**1. Find **** if **** and **** **

**Ans. **Given: and

Expanding along first row,

=

=

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

**Ans. **Given: and

On Adding = + =

On Subtracting = =

Therefore,

Expanding along first row =

=

Therefore, a unit vector perpendicular to both and is

= =

**3. If a unit vector **** makes an angle **** with **** **** with **** and an acute angle **** with **** then find **** and hence, the components of ****.**

**Ans. **Let be a unit vector. ……….(i)

Squaring both sides, ……….(ii)

Given: Angle between vectors and is

……….(iii)

Again, given Angel between vectors and is

……….(iv)

Again, given Angel between vectors and is where is acute angle.

……….(v)

Putting the values of and in eq. (ii),

Since is acute angle, therefore is positive and hence

From eq. (v),

Putting values of and in eq. (i),

Components of are coefficients of in

and angle

**4. Show that **** **

**Ans. **L.H.S. = =

= = = R.H.S.

**5. Find **** and **** if **** **

**Ans. **Given:

Expanding along first row,

=

Comparing the coefficients of on both sides, we have

……….(i)

……….(ii)

And ……….(iii)

From eq. (ii),

From eq. (iii),

Putting the values of and in eq. (i),

0 = 0

Therefore, and

**6. Given that **** and **** What can you conclude about the vectors **** and **** **

**Ans. **Given:

or or

or or vector is perpendicular to …..(i)

Again, given

or or

or or vector and are collinear or parallel. …..(ii)

Since, vectors & are perpendicular to each other as well as parallel are not possible. ..(iii)

Therefore, from eq. (i), (ii) and (iii), either or

and

**7. Let the vectors **** be given as **** then show that **** **

**Ans. **Given: Vector and

Now L.H.S. =

= +

[By Property of Determinants]= = R.H.S.

**8. It either **** and **** then **** Is the converse true? Justify your answer with an example.**

**Ans. **Given: Either or

or ……….(i)

[Using eq. (i)]

[By definition of zero vector]

But the converse is not true.

Let

is a non-zero vector.

Let

is a non-zero vector.

But

Taking 2 common from R_{3} = [ R_{2} and R_{3} are identical]

#### NCERT Solutions class 12 Maths Exercise 10.4

**9. Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).**

**Ans. **Vertices of are A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).

Position vector of point A = (1, 1, 2) =

Position vector of point B = (2, 3, 5) =

Position vector of point C = (1, 5, 5) =

Now = Position vector of point B – Position vector of point A

=

=

=

And = Position vector of point C – Position vector of point A

=

=

=

x =

= =

Now Area of triangle ABC =

= sq. units

#### NCERT Solutions class 12 Maths Exercise 10.4

**10. Find the area of the parallelogram whose adjacent sides are determined by the vectors **** **** and **** **

**Ans. **Given: Vectors representing two adjacent sides of a parallelogram are

and

= =

Now Area of parallelogram =

= sq. units

#### NCERT Solutions class 12 Maths Exercise 10.4

**11. Let the vectors **** and **** such that **** then **** is a unit vector, if the angle between **** and **** is:**

**(A) **

**(B) **

**(C) **

**(D) **

**Ans. **Given: and is a unit vector.

, where is the angle between and

Therefore, option (B) is correct.

#### NCERT Solutions class 12 Maths Exercise 10.4

**12. Area of a rectangle having vertices A, B, C and D with position vectors **** and **** respectively is:**

**(A) **

**(B) 1**

**(C) 2**

**(D) 4**

**Ans. **Given: ABCD is a rectangle.

Now = Position vector of point B – Position vector of point A

=

=

=

AB =

And = Position vector of point D – Position vector of point A

=

=

=

AD =

Area of rectangle ABCD = Length x Breadth = AB x AD = 2 x 1 = 2 sq. units

Therefore, option (C) is correct.

## NCERT Solutions class 12 Maths Exercise 10.4

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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Nice solution

Very stasficatory answer sir

Thanks a lot

Nice. Thanku sir