MP Board Class 12th Maths Important Questions Chapter 10 Vector Algebra

MP Board Class 12th Maths Important Questions Chapter 10 Vector Algebra

MP Board Class 12th Maths Important Questions Chapter 10 Vector Algebra

Important Questions

Very Short Answer Type Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 25.
If modulus of two vectors   and   are equal and angle between them is 60° and their dot product is  find their modulus? (CBSE 2018)
Solution:

Question 26.

Short Answer Type Questions

Question 1.

Question 3.
If G is centroid of ∆ABC, then prove that:

Question 4.
Using vectors prove that the medians of traiangle are concurrent?
Solution:
Let medium of ∆ABC are AD, BE and CF.

Question 5.
A vector , makes angle 45° with OX and 60° with OY. Find the angle made by  with OZ?
Solution:
Let angle made by vector O⃗ P with axes OX, OY and OZ are α, β, γ respectively. then
α = 45°,
β = 60°

Question 6.
Find the vector   which makes an angle with X – axis, F – axis and Z – axis respectively are  and angle θ and its magnitude is 5√2?
Solution:
Given:

Question 7.
Prove that:

Question 14.

Question 15.
If the angle between two unit vectors   and   is θ then prove that:

Question 16.
The angle between two vectors   and   is θ then prove that:

Question 17.
In any traiangle prove that ABC?
(A) ac cos B – bc cos A = a² – b²?
(B) 2(bc cos A + ca cos B + ab cos C) = a² + b² + c²?
Solution:

Question 18.
In ∆ABC prove by vector method c = acosB + bcosA?
Solution:
In ∆ABC

⇒ c² = ac cos B + bc cos A
⇒ c² = c(a cos B + b cos A)
⇒ c = a cos B + b cos A. Proved.

Question 19.
In ∆ABC prove by vector method
b² = a² + c² – 2ac cos B?
Solution:
In ∆ABC we know that

Question 20.
In ∆ABC Prove the following:
(A) a² = b² + c² – 2bc cos A?
(B) c² = a² + b² – 2ab cos C?
Solution:
Solve like Q.No. 19

Question 21.

Question 24.
By vector method prove that the square of the hypotenuse of a right angle triangle is equal to the sum of the square of the other two sides?
Solution:
Let OAB be a right angled triangle at O. Taking O as the origin. Let the position vector of and be a and b respectively then = and  =  and ∠BOA = 90°.
∴ .  = 0

Question 26.
(A) Prove that:

Solution:

(B) Prove that:

Question 27.
Prove that:

Question 28.
Two forces are represented by vectors  displace a particle from points (1,2,3) to point2? (5,4,1)? Find the work done by the forces?
Solution:

Question 29.

Question 30.
Alorce of 6 units along the direction of vector acts on a partical? The partical is displaced from point  Find the work done by the force?
Solution:
Unit vector parllel to vector

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