# NCERT Class 12-Mathematics: Chapter – 10 Vector Algebra Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 7**:

A vector has magnitude and direction ratios . Find the direction cosines and components of , given that makes an acute angle with .

**Answer**:

**Question 8**:

Find a vector of magnitude , which is perpendicular to both the vectors and .

**Answer**:

**Question 9**:

Find the angle between the vectors

**Answer**:

Let

We know that, angle between two vectors is given by

**Question 10**:

If show that Interpret the result geometrically?

**Answer**:

Area of the parallelograms formed by taking any two sides represented by and as adjacent are equal

**Question 11**:

Find the sine of the angle between the vectors and

**Answer**:

**Question 12**:

If A, B, C, D are the points with position vectors respectively, find the projection of

**Answer**:

**Question 13**:

Using vectors, find the area of the triangle ABC with vertices , and .

**Answer**:

**Question 14**:

Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.

**Answer**:

Let ABCD and ABFE are parallelogram on the same base AB and between the same parallel line AB and DF.

Let

Now, area of parallelogram of

Hence proved

**Question 15**:

Prove that in any triangle ABC, where a, b, c are the magnitudes of the sides opposite to the vertices A, B, C, respectively.

**Answer**:

Here, components of are C and is drawn.

Since,

In using Pythagoras theorem