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RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

May 25, 2019 by Fazal Leave a Comment

Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.5

Question 1.
Find the value of
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 2.
Prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 3.
Evaluate the formula
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 4.
For any vector \(\overrightarrow { a } \), prove that:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
We know that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 5.
Prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 6.
Prove that \(\overrightarrow { a } \),\(\overrightarrow { b } \),\(\overrightarrow { c } \) are coplanar if \(\overrightarrow { a } \) × \(\overrightarrow { b } \), \(\overrightarrow { b } \) × \(\overrightarrow { c } \), \(\overrightarrow { c } \) × [/latex], \(\overrightarrow { a } \) are coplanar
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 7.
Prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 8.
If magnitude of two \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are √3 and 2 respectively \(\overrightarrow { a } \) and. \(\overrightarrow { b } \) = √6, then find the angle between \(\overrightarrow { a } \) and \(\overrightarrow { b } \)
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 9.
Find the angle between the vectors
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 10.
Find the projection of vector
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 11.
Find projection vector on vector
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
on vector
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 12.
Find the value of
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 13.
Find the magnitude of two vectors \(\overrightarrow { a } \) and \(\overrightarrow { b } \), if their magnitude are equal and angle between them is 60° and their scalar product is \(\frac { 1 }{ 2 } \)
Solution:
According to question
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 14.
If for a vector \(\overrightarrow { a } \), (\(\overrightarrow { x } \) – \(\overrightarrow { a } \) ).( \(\overrightarrow { x } \) + \(\overrightarrow { a } \) ) = 12, then | \(\overrightarrow { x } \) |.
Solution:
According to question,
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 15.
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5
such that \(\overrightarrow { a } \) + λ \(\overrightarrow { b } \) is perpendicular on \(\overrightarrow { c } \), then find the value of λ.
Solution:
According to question \(\overrightarrow { a } \) + λ \(\overrightarrow { b } \) is a perpendicular to \(\overrightarrow { c } \)
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Question 16.
If vertices \(\overrightarrow { a } \), \(\overrightarrow { b } \), \(\overrightarrow { c } \) are such that
\(\overrightarrow { a } \) + \(\overrightarrow { b } \) + \(\overrightarrow { c } \) = \(\overrightarrow { 0 } \)
then, find the value of \(\overrightarrow { a } \) . \(\overrightarrow { b } \) + \(\overrightarrow { b } \) . \(\overrightarrow { c } \) + \(\overrightarrow { c } \) . \(\overrightarrow { a } \)
Solution:
According to question
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

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.
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

RBSE Solutions for Class 12 Maths

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