Question

Vector ä is 3m long and is 60° above x-axis in the first quadrant. Vector b is 5m long and is 50° below the x-axis in the fourth quadrant. Find ajä + b, ba-b, c) b-a. Provide answers to a)-c) in both, unit-vector notations and in terms of magnitude and direction For two vectors mentioned in the problem 3, find ab and axb (in terms of magnitude and direction). 3. 4.

Answer 1

a^vector = 3 cos 60 degrees i^^+ 3 sin 60 degrees j^^ b^vector = 5 cos 50 degrees i^^- 5 sin 50 degrees j^^ In Unit vector Notation: - (a) a^vector + b^vector = (3 cos 60 degrees + 5 cos 50 degrees)i^^+ (3 sin 60 degrees - 5 sin 50 degrees)j^^ = 4.7139 i^6 - 1.232 j^^ (b) a^vector - b^vector = (3 cos 60 degrees - 5 cos 50 degrees)i^^+ (3 sin 60 degrees + 5 sin 50 degrees)j^^ = -1.7139 i^^+ 6.428 j^^ (c) b^vector - a^vector = -(a^vector - b^vector) = 1.7139 i^6 - 6.428 j^^ \r\n Magnitude and Direction (a) a^vector + b^vector magnitude = squareroot (4.7139)^2 + (1.232)^2 = 4.8722 theta = tan^-1(-1.232/4.7139) = -14.646 degrees (- sign shows below x - axis in Fourth Quadrant) (b) a^vector - b^vector magnitude = squareroot 1.7319^2 + 6.428^2 = 6.6525 theta = tan^-1 (-1.7139/6.428) = 165 degrees from positive x - direction [Second Quadrant] (c) b^vector - a^vector magnitude