# 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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**NCERT Solutions for Class 12 Maths Vector Algebra Exercise 10.4**The PDF books of * NCERT Solutions for Class 12* are the first step towards the learning and understanding the each sections of Maths, Physics, Chemistry, Biology as it all help in engineering medical entrance exams. To solve it, you just need to click on download links of

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**CBSE NCERT Solutions for Class 12**^{th}Maths**can be downloaded in PDF file. The downloading link is given at last.**

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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)