Contents

# NCERT Solutions for Class 12 Maths Vector Algebra Miscellaneous Exercise

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

* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise. This*

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

*NCERT Solutions** NCERT Solutions for class 12* is highly recommended by the experienced teacher for students who are going to appear in

*and*

**CBSE Class 12***and*

**JEE Mains***and NEET level exams. Here You will get*

**Advanced***of all questions given in NCERT textbooks of class 12 in details with step by step process.*

**NCERT Solutions for Class 12 Maths Vector Algebra Miscellaneous Exercise*** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**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

**NCERT solutions for class 12**.

## NCERT Solutions for Class 12 Maths Vector Algebra Miscellaneous Exercise

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 1**

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 2**

Find the scalar components and magnitude of the vector joining the points P(x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}).

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 3**

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure..

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 4**

If **a** = **b** + **c**, then is it true that | **a** | = | **b** | + | **c** |? Justify your answer.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 5**

Find the value of x for which x(**i** + **j** + **k**) is a unit vector.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 6**

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors **a** = 2**i** + 3**j** – **k** and **b** = **i** – 2**j** + **k**.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 7**

If **a** = **i** + **j** + **k**, **b** = 2**i** – **j** + 3**k** and **c** = **i** – 2**j** + **k**, find a unit vector parallel to the vector 2**a** – **b** + 3**c**.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 8**

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 9**

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2**a** + **b**) and (**a** – 3**b**) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 10**

The two adjacent sides of a parallelogram are 2**i** − 4**j** + 5**k** and **i** − 2**j** − 3**k**. Find the unit vector parallel to its diagonal. Also, find its area.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 11**

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 12**

Let **a** = **i** + 4**j** + 2**k**, **b** = 3**i** – 2**j** + 7**k** and **c** = 2**i** – **j** + 4**k**. Find a vector **d** which is perpendicular to both **a** and **b**, and **c**.**d** = 15.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 13**

The scalar product of the vector **i** + **j** + **k** with a unit vector along the sum of vectors 2**i** + 4**j** − 5**k** and λ**i** + 2**j** + 3**k** is equal to one. Find the value of **λ**.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 14**

If **a**, **b**, **c** are mutually perpendicular vectors of equal magnitudes, show that the vector **a** + **b** + **c** is equally inclined to **a**, **b** and **c**.

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 15**

Prove that (**a** + **b**).(**a** + **b**) = |**a**|^{2} + |**b**|^{2}, if and only if **a**, **b** are perpendicular, given **a** ≠ **0** and **b** ≠ **0**.

**NCERT Solutions:**

Choose the correct answer in Exercises 16 to 19.

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 16**

If θ is the angle between two vectors **a** and **b**, then **a**⋅**b** ≥ 0 only when

(A) 0 < θ < π/2

(B) 0 ≤ θ ≤ π/2

(C) 0 < θ < π

(D) 0 ≤ θ ≤ π/2

**NCERT Solutions:**

(B)** a**⋅**b** ≥ 0 or, |a||b|cosθ ≥ 0 or cosθ ≥ 0 or 0 ≤ θ ≤ π/2

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 17**

Let **a** and **b** be two unit vectors and **θ** is the angle between them. Then **a** + **b** is a unit vector if

(A) θ = π/4

(B) θ = π/3

(C) θ = π/2

(D) θ = 2π/3

**NCERT Solutions:**

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 18**

The value of **i**.(**j** × **k**) + **j**⋅(**i** × **k**) + **k**⋅(**i** × **j**) is

(A) 0

(B) -1

(C) 1

(D) 3

**NCERT Solutions:**

(C)** i**.(**j** × **k**) + **j**⋅(**i** × **k**) + **k**⋅(**i** × **j**) = **i**.**i** + **j**⋅(**-j**) + **k**⋅**k** = 1 – 1 + 1 = 1

**NCERT Solutions Class 12 Math Vector Algebra Miscellaneous ****Exercise**** Ques No 19**

If θ is the angle between any two vectors **a** and **b**, then | **a** ⋅ **b** | = | **a** × **b** | when θ is equal to

(A) 0

(B) -1

(C) 1

(D) 3

**NCERT Solutions:**