Question

It is found that |A+B|=|A|.This necessarily implies,


(a) B = 0(b) A,B are antiparallel(c) A,B are perpendicular(d) A.B ≤ 0

Answer 1

Options (a) and (d) are correct.

question : It is found that |A + B| = |A|. this necessarily implies,

(a) B = 0

(b) A, B are antiparallel

(c) A, B are perpendicular

(d) A.B ≤ 0

solution : it is given that |A + B| = |A|

squaring both sides we get,

|A + B|² = |A|²

we know, |a + b| = a² + b² + 2abcosθ

so, |A + B|² = A² + B² + 2ABcosθ , where θ is angle between A and B.

now A² + B² + 2ABcosθ = A²

⇒B² + 2ABcosθ = 0

⇒B(B + 2Acosθ) = 0

so , B = 0 .......(1)

and B + 2Acosθ = 0.....(2)

now A.B = ABcosθ

= AB × -B/2A = -B² ≤ 0 [ from equation (2)]

so, A.B ≤ 0 .......(3)

from equations (1) and (3) we can see that options (1) and (4) are correct.

Answer 2

Answer:

B=O is the correct answer