if A=12x - 16y and B= - 24x + 10y,what is the magnitude of the vecror C=2A-B?
Please check out the necessity to solve them and thank
A(x) =12 , B(x) = - 24,
C(x)=(2A-B)(x)=(2•12-(-24)) =48
A(y) = -16, B(y) = 10.
C(y)=(2A-B)(y)=(2•(-16) -10) = - 42
Magnitude of C=2A-B =sqrt{48²+(-42)²} =63.78
To find the magnitude of the vector C = 2A - B, we need to substitute the given values for A and B into the equation for C and then calculate the magnitude.
Given:
A = 12x - 16y
B = -24x + 10y
Substituting these values into the equation for C:
C = 2A - B
= 2(12x - 16y) - (-24x + 10y)
= 24x - 32y + 24x - 10y
= 48x - 42y
To calculate the magnitude of vector C, we can use the formula for the magnitude of a 2-dimensional vector, which is the square root of the sum of the squares of its components:
Magnitude(C) = sqrt((48)^2 + (-42)^2)
Calculating this:
Magnitude(C) = sqrt(2304 + 1764)
= sqrt(4068)
≈ 63.82
Therefore, the magnitude of vector C is approximately 63.82.
To find the magnitude of vector C, we need to first find the value of vector C by substituting the given values of A and B into the equation C = 2A - B.
Let's substitute the values of A and B into the equation:
C = 2A - B
C = 2(12x - 16y) - (-24x + 10y)
C = 24x - 32y + 24x - 10y
C = 48x - 42y
Now that we have the value of vector C as 48x - 42y, we can calculate its magnitude using the formula:
|C| = √(x^2 + y^2)
Let's calculate the magnitude of vector C:
|C| = √((48)^2 + (-42)^2)
|C| = √(2304 + 1764)
|C| = √(4068)
|C| ≈ 63.82
Therefore, the magnitude of vector C is approximately 63.82.