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RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3

May 25, 2019 by Fazal Leave a Comment

Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.3

Question 1.
Find vector product of vectors
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 2.
Find perpendicular unit vector of vectors
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 3.
For vectors \overrightarrow { a } and \overrightarrow { b } , prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 4.
Prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Solution:
According to question,
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 5.
If \overrightarrow { a } , \overrightarrow { b } , \overrightarrow { c } are unit vectors, such that
\overrightarrow { a } . \overrightarrow { b } = 0 = \overrightarrow { a } . \overrightarrow { c } and angle between \overrightarrow { b } and \overrightarrow { c } is \frac { \pi }{ 6 } , then prove that \overrightarrow { a } = ± 2 (\overrightarrow { b } × \overrightarrow { c } )
Solution:
Given that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 6.
Find the value of
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Solution:
We know that if \overrightarrow { a } and \overrightarrow { b } are two vectors and θ is the angle between them, then
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 7.
Find vector perpendicular to the vectors
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
whose magnitude is 9 unit.
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Question 8.
Show that:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
also, explain geometrically.
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
= 2(vector area of parallelogram ABCD).
Thus we conclude that area of parallelogram whose adjacent sides are diagonals of given parallelogram is twice the area of given parallellogram.

Question 9.
For any vector \overrightarrow { a } , prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3

Question 10.
If two adjacent sides of a triangle are represented by vectors
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3
then find the area of triangle.
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3

RBSE Solutions for Class 12 Maths

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