For the three vectors A+B+C= -1.4i. Vector A is 4i and vector C is -2j.
Write vector B as components separated by a comma. 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.
To find vector B, we can rearrange the equation A+B+C = -1.4i and solve for B.
Given that vector A is 4i and vector C is -2j, we can substitute these values into the equation:
4i + B - 2j = -1.4i
Rearranging the terms, we can rewrite the equation as:
B = -1.4i - 4i + 2j
Combining like terms, we get:
B = (-1.4 - 4)i + 2j
Simplifying further:
B = -5.4i + 2j
Therefore, the components of vector B are -5.4 and 2, separated by a comma.
To find the magnitude of vector B, we can use the Pythagorean theorem. The magnitude of vector B can be calculated using the formula:
|B| = sqrt(Bx^2 + By^2)
where Bx and By are the x and y components of vector B, respectively.
Plugging in the values, we have:
|B| = sqrt((-5.4)^2 + 2^2)
= sqrt(29.16 + 4)
= sqrt(33.16)
≈ 5.75
So, the magnitude of vector B is approximately 5.75.
To find the angle above the negative x-axis that vector B points, we can use the inverse tangent function. The angle can be calculated using the formula:
θ = atan(By / Bx)
where By is the y-component of vector B and Bx is the x-component of vector B.
Plugging in the values, we have:
θ = atan(2 / -5.4)
≈ atan(-0.37)
≈ -21.21 degrees
Since the negative x-axis is at 180 degrees, we can add 180 degrees to the result to get the angle measured clockwise from the negative x-axis:
θ = -21.21 + 180
≈ 158.79 degrees
Therefore, vector B points approximately 158.79 degrees above the negative x-axis, measured clockwise.