# NCERT Class 12-Mathematics: Chapter –10 Vector Algebra Part 5

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**Question 20:**

The unit vector perpendicular to the vectors and forming a right handed system is

(A)

(B)

(C)

(D)

**Answer:**

(A) Is the correct answer.

Required unit vector is .

**Question 21:**

If then lies in the interval

(A)

(B)

(C)

(D)

**Answer:**

(A) Is the correct answer.

The smallest value of will exist at numerically smallest value of ., at , which gives

The numerically greatest value of is at which

## 10.3 EXERCISE

### Short Answer (S.A)

**Question 1:**

Find the unit vector in the direction of sum of vectors

**Answer:**

Let

**Question 2:**

If find the unit vector in the direction of

(i)

(ii)

**Answer:**

Here,

(i) Since,

(ii) Since,

**Question 3:**

Find a unit vector in the direction of , where P and Q have co-ordinates and , respectively.

**Answer:**

Since, the coordinates of are and , respectively.

**Question 4:**

If and are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that .

**Answer:**

**Question 5:**

Using vectors, find the value of *k* such that the points and are collinear.

**Answer:**

**Question 6:**

A vector is inclined at equal angles to the three axes. If the magnitude of is units, find .

**Answer:**