# 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 .

Question 8:

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

Question 9:

Find the angle between the vectors

Let

We know that, angle between two vectors is given by

Question 10:

If show that Interpret the result geometrically?

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

Question 12:

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

Question 13:

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

Question 14:

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

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.