Hello Students. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 10.3**.

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**NCERT Solutions for Maths Class 12 Exercise 10.1**

**NCERT Solutions for Maths Class 12 Exercise 10.2**

**NCERT Solutions for Maths Class 12 Exercise 10.4**

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**NCERT Solutions for Maths Class 12 Exercise 10.3**

**Maths Class
12 Ex 10.3 Question 1.**

Find the angle between two vectors ** a** and

**with magnitudes √3 and 2, respectively, having**

*b***.**

*a***= √6.**

*b***Solution:**

Let Î¸ be the angle between two vectors.

Given that ** a** = √3,

**= 2 and**

*b***.**

*a***= √6**

*b***Maths Class
12 Ex 10.3 Question 2.**

Find the angle between the vectors

**Solution:**

Let Î¸ be the angle between ** a** and

**.**

*b***Maths Class 12 Ex 10.3 Question 3.**

Find the projection of the vector ** i** –

**on the vector**

*j***+**

*i***.**

*j***Solution:**

**Maths Class
12 Ex 10.3 Question 4.**

Find the projection of the vector ** i** + 3

**+ 7**

*j***on the vector 7**

*k***–**

*i***+ 8**

*j***.**

*k***Solution:**

**Maths Class
12 Ex 10.3 Question 5.**

Show that each of the given three vectors is a unit vector.

Also, show that they are mutually perpendicular to each other.

**Solution:**

**Maths Class 12 Ex 10.3 Question 6.**

**| and |**

*a***|, if (**

*b***+**

*a***).(**

*b***–**

*a***) = 8 |**

*b***|.**

*b*

**Solution:**

**Maths Class
12 Ex 10.3 Question 7.**

**Solution:**

**Maths Class 12 Ex 10.3 Question 8.**

Find the magnitude of two vectors ** a** and

**, having the same magnitude and such that the angle between them is 60° and their scalar product is ½.**

*b***Solution:**

We have given that, |** a**| = |

**|, Î¸ = 60˚ and**

*b***.**

*a***= ½**

*b*We know that

**Maths Class
12 Ex 10.3 Question 9.**

Find |** x**|, if for a unit
vector

**Solution:**

Given that, ** a** is a unit vector, then |

**| = 1.**

*a***Maths Class 12 Ex 10.3 Question 10.**

If ** a** = 2

**+ 2**

*i***+ 3**

*j***,**

*k***= -**

*b***+ 2**

*i***+**

*j***and**

*k***= 3**

*c***+**

*i***are such that**

*j***+ Î»**

*a***is perpendicular to c, then find the value of Î».**

*b***Solution:**

**Maths Class
12 Ex 10.3 Question 11.**

Show that |** a**|

**+ |**

*b***|**

*b***is perpendicular to |**

*a***|**

*a***– |**

*b***|**

*b***, for any two non-zero vectors**

*a***and**

*a***.**

*b***Solution:**

**Maths Class
12 Ex 10.3 Question 12.**

If , then what can be concluded about
the vector ** b** ?

**Solution:**

This implies that, ** b** = 0

Hence,

**is any vector.**

*b***Maths Class
12 Ex 10.3 Question 13.**

If are the unit vector such that , then find the value of .

**Solution:**

**Maths Class
12 Ex 10.3 Question 14.**

If either vector, then. But the converse need not be true. Justify your answer with an example.

**Solution:**

**Maths Class
12 Ex 10.3 Question 15.**

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (-1, 0, 0),
(0, 1, 2), respectively, then find ∠ABC.
[∠ABC is the angle between the
vectors **BA** and **BC**.]

**Solution:**

**Maths Class
12 Ex 10.3 Question 16.**

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1) are
collinear.

**Solution:**

The position vectors of points A, B and C are:

**Maths Class
12 Ex 10.3 Question 17.**

Show that the vectorsform the vertices of a right angled triangle.

**Solution:**

The position vectors of the points A, B and C are:

**Maths Class 12 Ex 10.3 Question 18.**

If ** a** is
a non-zero vector of magnitude ‘

*a*’ and Î» is a non-zero scalar, then Î»

**is unit vector if**

*a*(A) Î» = 1

(B) Î» = – 1

(C)

*a*= |Î»|

(D)

*a*= 1/|Î»|

**Solution:**

Hence, the correct answer is option (D).

**Related Links:**

**NCERT Solutions for Maths Class 12 Exercise 10.1**