# NCERT Class 12-Mathematics: Chapter –10 Vector Algebra Part 7

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**Question 16:**

If determine the vertices of a triangle, show that gives the vector area of the triangle. Hence deduce the condition that the three points are collinear. Also find the unit vector normal to the plane of the triangle.

**Answer:**

**Question 17:**

Show that area of the parallelogram whose diagonals are given by is Also find the area of the parallelogram whose diagonals are and .

**Answer:**

**Question 18:**

If and find a vector such that and

**Answer:**

Let

And

For .

Also,

On adding Eq. (ii) and (iii), we get

On adding Eq. (iv) and (v), we get

Now,

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Exercises from 19 to 33 (M.C.Q)

**Question 19:**

The vector in the direction of the vector that has magnitude is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 20:**

The position vector of the point which divides the join of points and in the ratio is

(A)

(B)

(C)

(D)

**Answer: (D)**

**Question 21:**

The vector having initial and terminal points as and , respectively is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 22:**

The angle between two vectors and with magnitudes and , respectively, and is

(A)

(B)

(C)

(D)

**Answer: (B)**