# 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.**

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*and*

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**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

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**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

*.*

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**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:**