What is the magnitude of vector B? How many degrees above the negative x-axis does vector B point? Measure the angle clockwise from the negative x-axis.For the three vectors A+B+C= -1.4i. Vector A...

What is the magnitude of vector B?

How many degrees above the negative x-axis does vector B point?
Measure the angle clockwise from the negative x-axis.

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.

Asked on by blasto63

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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` .

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