Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.5
Question 1.
Find the value of
Solution:
Question 2.
Prove that
Solution:
Question 3.
Evaluate the formula
Solution:
Question 4.
For any vector , prove that:
Solution:
We know that
Question 5.
Prove that
Solution:
Question 6.
Prove that ,
,
are coplanar if
×
,
×
,
× [/latex],
are coplanar
Solution:
Question 7.
Prove that
Solution:
Question 8.
If magnitude of two and
are √3 and 2 respectively
and.
= √6, then find the angle between
and
Solution:
Question 9.
Find the angle between the vectors
and
Solution:
Question 10.
Find the projection of vector
Solution:
Question 11.
Find projection vector on vector
on vector
Solution:
Question 12.
Find the value of
Solution:
Question 13.
Find the magnitude of two vectors and
, if their magnitude are equal and angle between them is 60° and their scalar product is
Solution:
According to question
Question 14.
If for a vector , (
–
).(
+
) = 12, then |
|.
Solution:
According to question,
Question 15.
such that + λ
is perpendicular on
, then find the value of λ.
Solution:
According to question + λ
is a perpendicular to
Question 16.
If vertices ,
,
are such that
+
+
=
then, find the value of .
+
.
+
.
Solution:
According to question
Question 17.
If vectors/1, B, C of triangle ABC are (1, 2,3), (-1,0, 0,), (0, 1, 2) respectively, then find ∠ABC.
Solution:
Let O be the origin.
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