Find a vector of magnitude 7 in the direction of v = 12i - 5k

Solution:

The vector of magnitude 7 in the direction of v = 12i - 5k will be expressed as follows:

Let the vector of magnitude 7 be denoted by F

The vector F in the direction of v = 12i - 5k is expressed as a product of the magnitude of vector F and the unit vector in the direction of v as given below:

F = 7 × v/IvI

IvI = √(12)² + (5)²

IvI = √144 + 25

IvI = √169

IvI = 13

F = (7)[(12/13)i - (5/13)k)

Find a vector of magnitude 7 in the direction of v = 12i - 5k

Summary:

Vector of magnitude 7 in the direction of v = 12i - 5k is (7)[(12/13)i - (5/13)k)