NCERT Class 12 Maths
Chapter 10: Vector Algebra
12 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra — Exercise 10.4
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Find |a×b| for a=i−7j+7k, b=3i−2j+2k.
Question 2
Find a unit vector perpendicular to a+b and a−b, where a=(3,2,2), b=(1,2,−2).
Question 3
A unit vector makes angles π/3 with i, π/4 with j and acute θ with k. Find θ and its components.
Question 4
Prove (a−b)×(a+b)=2(a×b).
Question 5
Find λ,μ if (2i+6j+27k)×(i+λj+μk)=0.
Question 6
Given a·b=0 and a×b=0, what can be concluded?
Question 7
For component vectors a=(a₁,a₂,a₃), b=(b₁,b₂,b₃), c=(c₁,c₂,c₃), prove a×(b+c)=a×b+a×c.
Question 8
A zero factor gives a×b=0. Is the converse true?
Question 9
Find the area of triangle A(1,1,2), B(2,3,5), C(1,5,5).
Question 10
Find the parallelogram area for adjacent sides a=i−j+3k, b=2i−7j+k.
Question 11
Given |a|=3 and |b|=√2/3, which listed angle makes a×b a unit vector?
Question 12
Find the area of the rectangle with position vectors (−1,1/2,4),(1,1/2,4),(1,−1/2,4),(−1,−1/2,4).