For this problem, vectors in the text an- shown in boldface lather than with arr

Question

For this problem, vectors in the text an- shown in boldface lather than with arrows over them. Use the standard coordinate system: x horizontal with positive to the light, y vertical with positive up.) Five pans of vectors are shown. In each pair, the magnitude of the vectors A and B are given for which pair of vectors does the vector difference A - B not have a magnitude of 5? They all have magnitude 5 For the vectors C and D at the right, the difference vector D - C points in the direction up and to the left up and to the right down and to the left down and to the right

Explanation / Answer

(a)

A= A cos theta + A sin theta = 5 cos 60 i+ 5 sin 60 = 2.5 i + 4.33 j

B =- B cos theta+ B sin theta = -5 cos 60 + 5 sin 60 j= -2.5 i + 4.33 j

A-B =  ( 2.5 i + 4.33 j -(-2.5 i + 4.33 j)

= 5.0 i

magnitude of A-B = sqrt 5^2 = 5

(b)

A= -3 i

B = 4j

A-B = -3i-4 j

magnitude = sqrt (-3)^2 + (- 4)^2= 5.0

(c)

A= 3i

B = -2i

A-B = 3i-( -2i) = 5i

magnitude sqrt 5^2 = 5.0

(d)

A = A cos thea + B cos theta = 4 cos 45 + 4 sin 45= 2.82 i + 2.82 j

B = 1 cos 45 + 1 sin 45 = 0.707 i + 0.707 j

A- B = 2.11 i + 2.11 j

magnitude = sqrt ( 2.11)^2 + ( 2.11)^2 = 2.98 which is not equal to 5

so option (d) is correct answer

(e)

A= 4j

B = 3i

A-B = 4j- 3i

magnitude = sqrt 4^2 + ( -3)^2 = 5.0

As per guide lines I worked first problem kindly post remianing question in the next post

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