Given the following vectors, where Vector A is 6.3 meters and Vector B is 3.5 meters, determine the magnitude of the following vector sums: A+B, A-B, B-A

I tried to do magnitude such as A+B = square root (6.3)^2+(3.5)^2 = 7.2 then A-B = square root (6.3)^2-(3.5)^2 = 5.2 then got unreal answers on B-A when square root (3.5)^2-(6.3)^2 was put into the calc.

If vector component Vh is -8.50 units and Vv is 4.80 units, what is the magnitude and direction of Vector V?

just given arbitrary vectors of some magnitudes, there is no way to compute their sum or difference.

Unless you know the x- and y-components, you are stuck.

No way to solve?

Well, well, let's dive into these vector sums, shall we?

For A+B, we use the formula |A + B| = sqrt((|A| + |B|)^2), which gives us |A + B| = sqrt((6.3)^2 + (3.5)^2) ≈ 7.08 meters. That's the magnitude of the sum of Vector A and Vector B, folks!

Now, for A-B, we use the formula |A - B| = sqrt((|A| - |B|)^2), which gives us |A - B| = sqrt((6.3)^2 - (3.5)^2) ≈ 5.92 meters. That's the magnitude of the difference between Vector A and Vector B. Keep it up!

However, when it comes to B-A, we should swap the order of the vectors. So, |B - A| = sqrt((|B| - |A|)^2) = sqrt((3.5)^2 - (6.3)^2). Now, be careful here, because sometimes the math gods can throw tricky negative signs at you! If the result is a negative value, it means the magnitude is imaginary or "unreal," as you mentioned. So, in this case, the magnitude of B-A is not real.

Now, onto the next question! If Vector Vh is -8.50 units and Vv is 4.80 units, we can find the magnitude of Vector V using the Pythagorean theorem. |V| = sqrt((-8.50)^2 + (4.80)^2) ≈ 9.60 units. So, the magnitude of Vector V is approximately 9.60 units.

As for the direction of Vector V, we can use some trigonometry. We can find the angle θ by taking the arctan(Vv / Vh). In this case, θ ≈ arctan(4.80 / -8.50) ≈ -29.8 degrees. And there you have it, folks! The magnitude of Vector V is approximately 9.60 units, and its direction is roughly -29.8 degrees.

I hope that clears things up for you, and remember, don't let those unreal answers scare you off! Keep solving those vectors with confidence!

To determine the magnitude of a vector sum, you need to use the following formula:

Magnitude = sqrt((ax + bx)^2 + (ay + by)^2)

where ax and bx represent the x-components of vectors A and B, and ay and by represent the y-components of vectors A and B.

Let's solve the first problem using this formula:

Given Vector A = 6.3 meters and Vector B = 3.5 meters, we have:
ax = 6.3
bx = 3.5

For A + B, we add the components:

ay = 0 (since A is not moving vertically)
by = 0 (since B is not moving vertically)

Now we plug these values into the formula:

Magnitude of A + B = sqrt((6.3 + 3.5)^2 + (0 + 0)^2) = sqrt(9.8^2) = 9.8 meters

For A - B, we subtract the components:

ay = 0
by = 0

Using the same formula:

Magnitude of A - B = sqrt((6.3 - 3.5)^2 + (0 - 0)^2) = sqrt(2.8^2) = 2.8 meters

For B - A, we reverse the order of subtraction:

ay = 0
by = 0

Using the formula:

Magnitude of B - A = sqrt((3.5 - 6.3)^2 + (0 - 0)^2) = sqrt(-2.8^2) = 2.8 meters

As for the second question:

Given a vector Vh = -8.50 units and Vv = 4.80 units, we need to find the magnitude and direction of Vector V.

The magnitude can be found using the formula:

Magnitude = sqrt(Vh^2 + Vv^2) = sqrt((-8.50)^2 + (4.80)^2)

After calculating this, you would obtain the magnitude.

To find the direction of Vector V, you can use trigonometry. The angle can be determined by:

Angle = atan(Vv / Vh).

Using the angle calculated, you can conclude the direction of Vector V.