Vector A,with a magnitude of 23 units, points in the positive x direction. Adding vector B to vector A

Question

yields a resultant vector that points in the negative x direction with a magnitude of 8 units. What are the magnitude and direction of vector
B?

Answer 1

If you add a vector 'B' to vector 'A' such that the resultant is in the direction negative to 'A', then vector 'B' is also in the direction negative to 'A', and has a larger magnitude than A.

When vectors are in the same direction, you can just add them normally to obtain the magnitude of the resultant.

A + (-B) = -8

(The negative signs mean B and the resultant are in the negative direction of A)

=> 23 + (-B) = -8
=> -B = -31
=> B = 31

Answer 2

vector A = (23,0)
vector C = (x,0)
vector B = (-8,0)

v(A) + v(C) = v(B)
(23,0) + (x,0) = (-8,0)
(x,0) = (-31,0)
resultant has magnitude 31 in the negative x direction.

Answer 3

base on my calculation for the direction angle of vector, tan inverse(23/-8)is equal -70degree but the correct answer id 180 degree.Can you explain why 180 degree Arora?

Answer 4

tanθ₂ = (Bsinθ/(A + Bcosθ))

In this case,

θ = 180

So, tanθ = 0

And hence, you get the required direction using the formula for angle calculation.

Answer 5

Note that in this case, θ₂ is equal to tan-1(0), which is actually zero, not 180.

But because the larger vector is B,

the formula is θ₂ = (Asinθ/(B + Acosθ)), which gives you an angle of 0 with B, which means an angle of 180 with A.

Answer 6

A + B = -8.
23 + B = -8,
B = -31 Units = 31 Units, West.