NCERT Class 12 Maths
Chapter 10: Vector Algebra
18 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra — Exercise 10.3
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Find the angle for |a|=√3, |b|=2 and a·b=√6.
Question 2
Find the angle between i−2j+3k and 3i−2j+k.
Question 3
Find the projection of \(\left[\begin{matrix}1\\-1\\0\end{matrix}\right]\) on \(\left[\begin{matrix}1\\1\\0\end{matrix}\right]\).
Question 4
Find the projection of \(\left[\begin{matrix}1\\3\\7\end{matrix}\right]\) on \(\left[\begin{matrix}7\\-1\\8\end{matrix}\right]\).
Question 5
Show (2,3,6)/7, (3,−6,2)/7, (6,2,−3)/7 are unit vectors and mutually perpendicular.
Question 6
Find |a|,|b| if (a+b)·(a−b)=8 and |a|=8|b|.
Question 7
Expand (3a−5b)·(2a+7b).
Question 8
Vectors a,b have equal magnitude, angle 60° and a·b=1/2. Find their magnitudes.
Question 9
For a unit vector a, (x−a)·(x+a)=12. Find |x|.
Question 10
For a=(2,2,3), b=(−1,2,1), c=(3,1,0), find λ if a+λb is perpendicular to c.
Question 11
Show |a|b+|b|a is perpendicular to |a|b−|b|a for nonzero a,b.
Question 12
If a·a=0 and a·b=0, what follows about b?
Question 13
Unit vectors a,b,c satisfy a+b+c=0. Find a·b+b·c+c·a.
Question 14
A zero factor gives a·b=0. Show the converse need not hold.
Question 15
Find ∠ABC for A(1,2,3), B(−1,0,0), C(0,1,2).
Question 16
Show A(1,2,7), B(2,6,3), C(3,10,−1) are collinear.
Question 17
Show the points with position vectors (2,−1,1),(1,−3,−5),(3,−4,−4) form a right-angled triangle.
Question 18
For nonzero vector a of magnitude a and nonzero scalar λ, when is λa a unit vector?