If a vector A= -5.0x-4.0y and vector B = -3.0x+8.0y, then the magnitude of vector C= A-B is
a. 13.4
b. 12.2
c. 148
d. 7.2
e. 4.5
-5 - -3 = -2
-4 - 8 = -12
sqrt (4 +144) = 12.2
Well, A and B are both vectors, so let's subtract them and find the magnitude of the result, vector C. We have:
C = A - B = (-5.0x - 4.0y) - (-3.0x + 8.0y)
= -5.0x - 4.0y + 3.0x - 8.0y
= -2.0x - 12.0y
Now, to find the magnitude of vector C, we can use the Pythagorean theorem, which states that the magnitude of a vector in two dimensions is given by:
|C| = sqrt((C_x)^2 + (C_y)^2)
Plugging in the values for C, we get:
|C| = sqrt((-2.0)^2 + (-12.0)^2)
= sqrt(4.0 + 144.0)
= sqrt(148.0)
≈ 12.166
So, the magnitude of vector C is approximately 12.166. But hey, let's round it up for some extra fun! So the answer is **b. 12.2**. Now that's how you calculate vectors with a smile!
To find the magnitude of vector C = A - B, we need to subtract the components of vector B from the components of vector A.
Given:
Vector A = -5.0x - 4.0y
Vector B = -3.0x + 8.0y
Subtracting the x-components:
A - B = -5.0x - (-3.0x) = -5.0x + 3.0x = -2.0x
Subtracting the y-components:
A - B = -4.0y - 8.0y = -12.0y
Now we have the vector C = -2.0x - 12.0y.
The magnitude of vector C is given by the formula:
|C| = sqrt((-2.0)^2 + (-12.0)^2)
Calculating:
|C| = sqrt(4 + 144)
|C| = sqrt(148)
|C| ≈ 12.1655
Therefore, the magnitude of vector C ≈ 12.2 (option b).
To find the magnitude of vector C, which is the difference of vectors A and B, we need to perform vector subtraction using the components of A and B.
Vector subtraction is done by subtracting the corresponding components of the vectors. In this case, we have:
C = A - B = (-5.0x - 4.0y) - (-3.0x + 8.0y)
To subtract the x-components, we have:
-5.0x - (-3.0x) = -5.0x + 3.0x = -2.0x
To subtract the y-components, we have:
-4.0y - 8.0y = -12.0y
So vector C is given by C = -2.0x - 12.0y.
Now, to find the magnitude of vector C, we use the formula:
|C| = sqrt((Cx)^2 + (Cy)^2)
Substituting the x and y components of C into the formula, we get:
|C| = sqrt((-2.0)^2 + (-12.0)^2)
Calculating the magnitudes, we have:
|C| = sqrt(4 + 144)
|C| = sqrt(148)
Therefore, the magnitude of vector C is approximately 12.17.
Comparing this value to the given options, we find that none of the options exactly match the calculated value. However, the closest option is b. 12.2.