For the vectors A and b use the method of components to find the magnitude and d

Question

For the vectors A and b use the method of components to find the magnitude and direction of the following. (The length of vector A is 9.10 m, and the length of B vector is 17.40 m.) (a) the vector sum A + B magnitude [10.55 ] m direction [34.46 ] degree counterclockwise from the + x - axis (b) the vector sum B + A magnitude [10.55] m degree counterclockwise from the + x - axis direction 34.46 (c) the vector difference vector A - B Magnitude [ ] x m direction [ ] degree counterclockwise from the +x-axis

Explanation / Answer

A = 9.10 m

B = 17.40 m

Resolving Forces in X direction for B -

Fx = B sin(30) (towards +ve X axis)

Fx =  17.40 * 0.5

Fx = 8.7 m (towards +ve X axis)

Resolving Forces in Y direction for B -

Fy = B cos(30)

Fy = 15.06  towards +ve Yaxis

Now ,

(c)

A - B = A + (- B)

This means direction of B will be be opposite to the given direction i.e Fx will act in -ve X axis and Fy will act in -ve Y axis .

Resolving Forces in X Direction =

Fx = 8.7 m (towards -ve X axis)

Resolving Forces in Y Direction =

Fy = 15.06 + 9.10

Fy = 24.16 (towards -ve Y axis )

F = Sqrt(Fx^2 + Fy^2)

F = 25.68 m

theta = tan^-1(8.7/24.16)

theta = 19.80

For A - B,
Magnitude = 25.68 m
Direction = 250.2 Counterclockwise from the +ve X axis.

(d)

B - A = B + (- A)

This means direction of A will be be opposite to the given direction i.e Fya will act in +ve Y axis.   

Resolving Forces in X Direction =

Fx = 8.7 m (towards +ve X axis)

Resolving Forces in Y Direction =

Fy = 15.06 + 9.10

Fy = 24.16 (towards +ve Y axis )

F = Sqrt(Fx^2 + Fy^2)

F = 25.68 m

theta = tan^-1(8.7/24.16)

theta = 19.80

For B - A,
Magnitude = 25.68 m
Direction = 70.2 Counterclockwise from the +ve X axis.

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