What are thr magnitude and direction of the resultant vector, R, when parallelog

Question

What are thr magnitude and direction of the resultant vector, R, when parallelogram law is apolied to A and B? of Part A-Geometric addition What are the magnitude and direction of the resultant vector, R, when the parallogram law s applied to A and B? Four vectors A, B, C, and D are shown (not to an angle of 16.5 degrees with respect to the positive x axos. Vector B has acts at an angle of 67.5 degrees with respect to the positive x axis. Vector C has acts at an angle of 150.1 degrees with respect to A has magnitude 18.5 and acts at 11.9 and 45.9 and Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive x axis. Separate your answers by a comma. Hints and acts at an angle of 287.1 degrees with respect to the positive x axis RAR = Give Up Incorrect, Try Again;5 attempts remaining Part B-Component addition of vectors What is the resultant vector, R, obtained by adding vectors C and D? Express the magnitude to three significant figures. Express the angle to one decimal pl lace, measured from the positive x axis. Separate your answers by a comma.

Explanation / Answer

Part A:

vector A = 18.5cos16.5i+18.5sin16.5j = 17.74i+5.25j

vector B =11.9cos67.5i+11.9sin67.5j = 4.55i+10.99j

Vector addition of A and B gives 17.74i+5.25j+4.55i+10.99j = 22.29i+16.24j

Magnitude of vector = sqrt(22.292+16.242) = 27.59

Part B:

vector C = -45.9cos29.9i+45.9sin29.9j = -39.79i+22.88j

vector D =15cos72.9i-15sin72.9j = 4.41i-14.34j

Vector addition of C and D gives  -39.79i+22.88j+4.41i-14.34j = -35.38i+8.54j

Magnitude of vector = sqrt(35.382+8.542) = 36.40

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