What is the magnitude of vector B?
For the three vectors A+B+C= -1.4i. Vector A is 4i and vector C is -2j. What is vector B?
Write vector B as components separated by a comma.
You should substitute the given vectors in the condition provided by the problem such that:
`bar A + barB + bar C = -1.4 bar i`
`4bar i + (a*bar i + b*bar j) - 2 bar j = -1.4 bar i`
`(4+a)bar i + (b - 2)bar j = -1.4 bar i`
Equating the coefficients of like unit vectors yields:
`4 + a = -1.4 => a = -1.4 - 4 => a = -5.4`
`b - 2 = 0 => b = 2`
You may write the vector `bar B = -5.4 bar i + 2 bar j` such that:
`bar B <-5.4 , 2>`
You need to evaluate the magnitude of the vector bar B such that:
`|bar B| = sqrt((-5.4)^2 + 2^2) => |bar B| = sqrt(29.16 + 4)`
`|bar B| ~~ 5.758`
Hence, evaluating the magnitude of the vector `bar B` yields `|bar B| ~~ 5.758` .
You need to evaluate the angle `alpha` made by the vector `bar B` to x axis such that:
`tan alpha = -5.4/2` => `tan alpha = -2.7 => alpha = pi - tan^(-1)(2.7) => alpha ~~ 110^o` (measured clockwise `~~ 69^o` )
Hence, evaluating angle `alpha` made by the vector `bar B` to negative x axis, measured clockwise yields `alpha` `~~ 69^o` .