Question

The rectangular components of a vector are (2, 2). The corresponding rectangular components of another
vector are (1, 3 ). Find the angle between the two vectors

Answer 1

V1 = 2i +2j .

V2 = 1i + √3 j .

V1 . V2 = |V1||V2| cos A (angle between two vector) .

(2i +2j)(i+ √3 j ) =2√2 ×2× cosA.

=> 2+2√3 = 4√2 cosA .

=> (1+√3)/2√2 = cosA .

=> 1/2 × 1/√2 + 1/√2 ×√3/2 = cos A .

=> cos(60 - 45)° = cos(A) .

=> cos (15°) = cos(A) .

=> A= 15° .

Hope this will help you .