Question

2013
Two vectors A and B are such that A+B=č
and A? + B2 = c ir is the angle between
positive direction of A and B then is:
(a) 8 = 0
(b)
(c) =
(d) 8 =
T: 0-9 A B
in​

Answer 1

Answer:

Since you have given options, short solution to this is:

12, 5 and 13 are right triangle triplets i.e. 144 + 25 = 169, clearly ABC can form a right angled triangle.

Given in the statement, A + B = C, with respect to vectors, A and B are height - base pair.

This brings us to the conclusion that: Angle between A and B must be 90deg or pi/2.

PS: The question has 2 same options. (typo?).

Note: This is just to come up with a solution with MCQ. This is not the correct/proper solution/explanation.

Proper solution:

Given,

m(A) = 12, m(B) = 5, m(C) = 13, where m(X) stands for magnitude of X.

A + B = C

squaring both sides,

A.A+ B.B + 2 A.B = C.C

note 'dot’ product i.e. A.A is equal to m(A)ˆ2.

=> m(A)ˆ2 + m(B)ˆ2 + 2 m(A)m(B)cos(ab) = m(C)ˆ2 , where ab is the angle between A and B.

Substituting the values in the above equation,

=> 144 + 25 + 60cos(ab) = 169

=> 169 + 60cos(ab) = 169

=> 60cos(ab) = 0

=> cos(ab) = 0

=> cos(ab) = cos(pi/2) or cos(90deg)

ab = pi/2 or 90deg, where ab is the angle between A and B.