**NCERT Solutions for Maths Class 12 Exercise 10.2**.

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**NCERT Solutions for Maths Class 12 Exercise 10.1**

**NCERT Solutions for Maths Class 12 Exercise 10.3**

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

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**NCERT Solutions for Maths Class
12 Exercise 10.2**

**Maths Class
12 Ex 10.2 Question 1.**

Compute the magnitude of the following vectors:

**Solution:**

**Maths Class
12 Ex 10.2 Question 2.**

Write two different vectors having same magnitude.

**Solution:**

**Maths Class
12 Ex 10.2 Question 3.**

Write two different vectors having same direction.

**Solution:**

Let the two vectors are:

Hence, vectorshave
the same direction but different magnitude.

**Maths Class
12 Ex 10.2 Question 4.**

Find the values of *x* and
*y* so that the vectors are equal.

**Solution:**
If vectors are equal, then their respective components are also equal.

On comparing the components in both the vectors, we get *x* = 2, *y* = 3.

**Maths Class
12 Ex 10.2 Question 5.**

Find the scalar and vector components of the vector with initial
point (2, 1) and terminal point (–5, 7).

**Solution:**

Let A (2, 1) be the initial point and B (–5, 7) be the terminal
point.

**Maths Class
12 Ex 10.2 Question 6.**

Find the sum of the vectors

**Solution:**

We have,

Thus, the sum of the vectors is

**Maths Class
12 Ex 10.2 Question 7.**

Find the unit vector in the direction of the vector .

**Solution:**

**We are given that**

**Maths Class 12 Ex 10.2 Question 8.**

Find the unit vector in the direction of vector , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

**Solution:**

The points P and Q are (1, 2, 3) and (4, 5, 6), respectively.

**Maths Class 12 Ex 10.2 Question 9.**

For given vectors, , find the unit vector in the direction of the vector .

**Solution:**

We are given that

**Maths Class
12 Ex 10.2 Question 10.**

Find a vector in the direction of vector which has magnitude 8 units.

**Solution:**

Let the given vector is

**Maths Class 12 Ex 10.2 Question 11.**

Show that the vectors are collinear.

**Solution:**

**Let the given vectors
are**

**Since both the vectors have the same direction, they are collinear.**

**Maths Class
12 Ex 10.2 Question 12.**

Find the direction cosines of the vector .

**Solution:**

Let

Here, a = 1, b = 2, c = 3

**Maths Class 12 Ex 10.2 Question 13.**

Find the direction cosines of the vector joining the points A (1, 2,
–3) and B (–1, –2, 1), directed from A to B.

**Solution:**

Vector joining the points A and B is

**Maths Class
12 Ex 10.2 Question 14.**

Show that the vector are equally inclined to the axes OX, OY, OZ.

**Solution:**

Let ,
Direction cosines of vector are

This shows that the given vector is equally inclined to the axes OX, OY, OZ.

**Maths Class 12 Ex 10.2 Question 15.**

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are respectively, in the ratio 2 : 1

(i) internally

(ii) externally.

**Solution:**

(i) The point R which divides the line joining the pointsin
the ratio m : n

**Maths Class 12 Ex 10.2 Question 16.**

Find the position vector of the midpoint of the vector joining the
points P (2, 3, 4) and Q (4, 1, –2).

**Solution:**

**Maths Class
12 Ex 10.2 Question 17.**

Show that the points A, B and C with position vectors, , respectively form the vertices of a right angled triangle.

**Solution:**

**Maths Class 12 Ex 10.2 Question 18.**

In triangle ABC (figure), which of the following is not true:

**Solution:**

Using vectors law, we have

Hence, the correct answer is option (C).

**Maths Class
12 Ex 10.2 Question 19.**

If are two collinear vectors, then which of the following are incorrect:

(B)

(C) the respective components of are
proportional.

(D) both the vectors have same direction, but different magnitudes.

**Solution:**

Since both the vectors ,
being collinear, are not necessarily in the same direction. They may have
opposite directions. Their magnitudes may be different.

Hence, the correct answer is option (D).

**Related Links:**

**NCERT Solutions for Maths Class 12 Exercise 10.1**