Vector A has a given magnitude of |A| = 3J and points due East. Vector B of unkn

Question

Vector A has a given magnitude of |A| = 3J and points due East. Vector B of unknown magnitude points directly North. The sum A + B makes an angle of 6 = 57 degrees North of East. Randomized Variables |A| = 35 6 =57 degrees 33% Part (a) Write an expression for the magnitude of vector B in terms of the magnitude of A, |A|, and the angle 6, using any required trigonometric functions. 33% Part (b) What is the numerical value for the magnitude of the difference of vectors A and B, |A - B|? 33% Part (c) What is the numerical value for the magnitude of the sum of vectors A and B, |A + B|?

Explanation / Answer

here we know

vector A = |A| i = 3.5 i

vector B = |B| j

A + B makes direction 57 deg norht to east

so tan(57) = |B|/|A|

a) magnitude of B = |B| = |A|*tan(57)

|B| = 3.5*1.54 = 5.39

vector B = 5.39 j

b)

vector A - B = 3.5 i - 5.39 j

magnitude of vector A - B = sqrt(5.39^2 + 3.5^2) = 6.43

c)

vector A + B = 3.5 i + 5.39 j

magnitude of vector A + B = sqrt(5.39^2 + 3.5^2) = 6.43

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