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.

Components of C Are CcosA and CSinA is Drawn

Since,

In using Pythagoras theorem