Hello Students. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 10.4**.

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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 10.3**

** **

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

**Maths Class
12 Ex 10.4 Question 1.**

Find |** a** ×

**|, if**

*b***=**

*a***– 7**

*i***+ 7**

*j***and**

*k***= 3**

*b***– 2**

*i***+ 2**

*j***.**

*k***Solution:**

We have given that, ** a** =

**– 7**

*i***+ 7**

*j***and**

*k***= 3**

*b***– 2**

*i***+ 2**

*j*

*k***Maths Class
12 Ex 10.4 Question 2.**

Find a unit vector perpendicular to each of the vector ** a**
+

**and**

*b***–**

*a***, where**

*b***= 3**

*a***+ 2**

*i***+ 2**

*j***and**

*k***=**

*b***+ 2**

*i***– 2**

*j***.**

*k***Solution:**

We have given that, ** a** = 3

**+ 2**

*i***+ 2**

*j***and**

*k***=**

*b***+ 2**

*i***– 2**

*j*

*k*Therefore,

**+**

*a***= (3**

*b***+ 2**

*i***+ 2**

*j***) + (**

*k***+ 2**

*i***– 2**

*j***) = 4**

*k***+ 4**

*i*

*j*And ** a** –

**= (3**

*b***+ 2**

*i***+ 2**

*j***) – (**

*k***+ 2**

*i***– 2**

*j***) =**

*k***+ 4**

*i*

*k***Maths Class
12 Ex 10.4 Question 3.**

If a unit vector ** a** makes
angles Ï€/3 with

**, Ï€/4 with**

*i***and an acute angle Î¸ with**

*j***, then find Î¸ and hence the components of**

*k***.**

*a***Solution:**

Let ** a** =

*a*_{1}

**+**

*i*

*a*_{2}

**+**

*j*

*a*_{3}

**such that**

*k***= 1**

*a***Maths Class
12 Ex 10.4 Question 4.**

Show that (** a** –

**) × (**

*b***+**

*a***) =**

*b***2**(

**×**

*a***)**

*b*

**Solution:**

**Maths Class
12 Ex 10.4 Question 5.**

**Solution:**

**Maths Class
12 Ex 10.4 Question 6.**

Given that ** a**.

**= 0 and**

*b***×**

*a***= 0. What can you conclude about the vectors**

*b***and**

*a***?**

*b***Solution:**

**Maths Class
12 Ex 10.4 Question 7.**

Let the vectors ** a**,

**,**

*b***be given as**

*c*

*a*_{1}

**+**

*i*

*a*_{2}

**+**

*j*

*a*_{3}

**,**

*k*

*b*_{1}

**+**

*i*

*b*_{2}

**+**

*j*

*b*_{3}

**,**

*k*

*c*_{1}

**+**

*i*

*c*_{2}

**+**

*j*

*c*_{3}

**. Then show that**

*k***× (**

*a***+**

*b***) =**

*c***×**

*a***+**

*b***×**

*a***.**

*c***Solution:**

**Maths Class
12 Ex 10.4 Question 8.**

If either ** a** = 0 or

**= 0, then**

*b***×**

*a***= 0. Is the converse true? Justify your answer with an example.**

*b***Solution:**

**Maths Class
12 Ex 10.4 Question 9.**

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

**Solution:**

**Maths Class
12 Ex 10.4 Question 10.**

Find the area of the parallelogram whose adjacent sides are
determined by the vectors ** a** =

**–**

*i***+ 3**

*j***and**

*k***= 2**

*b***– 7**

*i***+**

*j***.**

*k***Solution:**

**Maths Class
12 Ex 10.4 Question 11.**

Let the vectors ** a** and

**be such that |**

*b***| = 3 and |**

*a***| = √2/3, then**

*b***×**

*a***is a unit vector, if the angle between**

*b***and**

*a***is**

*b*(A) Ï€/6 (B) Ï€/4 (C) Ï€/3 (D) Ï€/2

**Solution:**

We have given that

Hence, the correct answer is option (B).

**Maths Class
12 Ex 10.4 Question 12.**

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

(A) ½ (B) 1 (C) 2 (D) 4

**Solution:**

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