Question

2.
The magnitude of scalar product of two vectors is 8 and that of vector product is 8/3. The angle between them is:
(A) 30°
(B) 60°
(C) 90°
(D) 150°​

Answer 1

Answer :

[Note : There should be 8/√3 in the question.]

Magnitude of scalar product = 8

Magnitude of vector product = 8/√3

We have to find angle between both vectors$.$

◈ Let two vectors A and B are inclined at an angle Φ.

◕ Scalar product of two vectors :

• A ▪ B = AB cosΦ

◕ Vector quantity of two vectors :

• A × B = AB sinΦ

ATQ,

AB cosΦ = 8 ➝ (equation : 1)

AB sinΦ = 8/√3 ➝ (equation : 2)

Taking ratio of 2 and 1, we get

⇒ AB sinΦ / AB cosΦ = (8/√3) / 8

⇒ tanΦ = 1/√3

⇒ Φ = 30°

Answer 2

Explanation:(1) a.b=8 this means a b cos theta is equal to 8 (2)a x b equal to 8 by 3 means

a b sin theta is equal to 8 by 3

(3) solving (1) & (2)

tan theta equal to 3

(4) theta is equal to tan inverse 1/3

Answer: tan-¹(1/3)= 20