Find the vector in the direction of the given vector A(5i-12j) and magnitude 39 units
To find a vector in the same direction as vector A(5i-12j) with a magnitude of 39 units, we need to scale the original vector by a factor that will result in the desired magnitude.
First, we calculate the magnitude of the vector A:
|A| = sqrt((5^2) + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13
Next, we calculate the scaling factor:
scaling factor = desired magnitude / |A| = 39 / 13 = 3
Now, we scale the original vector A by the scaling factor:
new vector = 3 * A = 3(5i - 12j) = 15i - 36j
Therefore, the vector in the direction of vector A(5i-12j) with a magnitude of 39 units is 15i - 36j.