# NCERT Solutions for Class 12 Maths Vector Algebra

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Vector Algebra Exercise 10.4*.

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*.*

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**CBSE Class 12**^{th}MathsNote: In this solution, the vector is represented by **BOLD** font. For example: **a**, **b,** **OP**, **AB, i, j, k** represent the vectors

## NCERT Solutions for Class 12 Maths Vector Algebra

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 1.**

Find | **a** × **b** |, if **a** = **i** − 7**j** + 7**k** and **b** = 3**i** − 2**j** + 2**k**.

**NCERT Solutions:**

Given that **a** = **i** − 7**j** + 7**k** and **b** = 3**i** − 2**j** + 2**k**.

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 2.**

Find a unit vector perpendicular to each of the vector (a + b) and (a − b), where **a** = 3**i** + 2**j** + 2**k** and **b** = **i** + 2**j** − 2**k**.

**NCERT Solutions:**

Given that **a** = 3**i** + 2**j** + 2**k** and **b** = **i** + 2**j** − 2**k**.

Thus, (**a** + **b**) = (3**i** + 2**j** + 2**k**) + (**i** + 2**j** − 2**k**) = (4**i** + 4**j**) and

(**a** − **b**) = (3**i** + 2**j** + 2**k**) − (**i** + 2**j** − 2**k**) = (**i** + 4**k**)

Thus, the unit vectors perpendicular to both the vectors (**a** + **b**) and (**a** + **b**) is

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 3.**

If a unit vector a makes angles π/3 with **i**, π/4 with **j** and an acute angle θ with **k**, then find θ and hence components of **a**.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 4.**

Show that (**a** − **b**) × (**a** + **b**) = 2(**a** × **b**).

**NCERT Solutions:**

LHS = (**a** − **b**) × (**a** + **b**)

= (**a** × **a**) + (**a** × **b**) − (**b** × **a**) − (**b** × **b**)

= (**0**) + (**a** × **b**) − [−(**a** × **b**)] − (**0**) {Since (**a** × **a**) = (**b** × **b**) = 0 and (**b** × **a**) = −(**a** × **b**)}

= (**a** × **b**) + (**a** × **b**) = RHS

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 5.**

Find λ and μ if (2**i** + 6**j** + 27**k**) × (**i** + λ**j** + μ**k**) = 0.

**NCERT Solutions:**

Given that **a** = (2**i** + 6**j** + 27**k**) and **b** = (**i** + λ**j** + μ**k**).

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 6.**

Given that **a **⋅ **b** = 0 and **a** × **b** = 0. What can you conclude about the vectors **a** and **b**?

**NCERT Solutions:**

Given that **a **⋅ **b** = 0 and **a** × **b** = 0

⇒ **a** = 0 or **b** = 0 or **a** ⟂ **b **

and

**a** = 0 or **b** = 0 or **a** || **b**

⇒ Either a = 0 or b = 0 (Since **a** ⟂ **b **and **a** ⟂ **b **are not true at same time.)

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 7.**

Let the vectors **a**, **b**, **c** given as a_{1}**i** + a_{2}**j** + a_{3}**k**, b_{1}**i** + b_{2}**j** + b_{3}**k**, and c_{1}**i** + c_{2}**j** + c_{3}**k**, Then show that **a** × (**b** + **c**) = (**a** × **b**) + (**a** × **c**).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 8.**

If either **a** = 0 or **b** = 0, then **a** × **b** = 0. Is the converse true? Justify your answer with an example.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 9.**

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

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 10.**

Find the area of the parallelogram whose adjacent sides are determined by the vectors **a** = **i** − **j** + 3**k** and **b** = 2**i** − 7**j** + **k**.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 11.**

Let the vectors **a** and **b** be such that |**a**| = 3 and |**b**| = √2/3, then **a** × **b** is a unit vector, if the angle between **a** and **b** is

(A) π/6

(B) π/4

(C) π/3

(D) π/2

**NCERT Solutions:**

(B) Since |**a** × **b**| = |**a**||**b**|sinθ

⇒

**NCERT Solutions for Class 12 Maths Vector Algebra ****Exercise**** 10.4: Ques No 12.**

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

, respectively is

(A) 1/2

(B) 1

(C) 2

(D) 4

**NCERT Solutions:**

(C)