Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.3
Question 1.
Find vector product of vectors
and
Solution:
Question 2.
Find perpendicular unit vector of vectors
and
Solution:
Question 3.
For vectors and
, prove that
Solution:
Question 4.
Prove that
Solution:
According to question,
Question 5.
If ,
,
are unit vectors, such that
.
= 0 =
.
and angle between
and
is
, then prove that
= ± 2 (
×
)
Solution:
Given that
Question 6.
Find the value of
Solution:
We know that if and
are two vectors and θ is the angle between them, then
Question 7.
Find vector perpendicular to the vectors
and
whose magnitude is 9 unit.
Solution:
Question 8.
Show that:
also, explain geometrically.
Solution:
= 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 , prove that
Solution:
Question 10.
If two adjacent sides of a triangle are represented by vectors
and
then find the area of triangle.
Solution:
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