Question

If A x B= 0 and A.B=-AB, then angle
between A and B is...
(A) 0°
(B) 45°
(C) 90°
(D) 180°​

Answer 1

Answer:

B)45⁰

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Answer 2

Answer:

If A x B= 0 and A.B=-AB, then the angle between A and B is 0°.

Step-by-step explanation:

Here, A and B are two vectors.

(A × B) is the cross product of vectors A and B. The formula/identity for the cross product is:

(A × B) = |A||B| sinφ

∵ (A × B) = 0 (given)

∴ |A||B| sinφ = 0..........(i)

⇒ |A||B| sinφ = |A||B| sin0°

⇒ sinφ = sin0°

⇒ φ = 0° [By comparing we get]

Again, (A.B) is the dot product of the vectors A and B. The formula/identity for the dot product is:

(A.B) = |A||B| cosφ

∵ A.B = -AB (given)

∴ |A||B| cosφ = -A.B

⇒ |A||B| cos |A||B| cosφ = |A||B| cos360°

⇒ cosφ = cos360°

⇒ φ = 360°

Now, 360° is equivalent to 0° since they are at the same point.

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