Question

Find unit vectors that satisfy the given conditions:

The unit vector in the same direction as ⟨−3,−5⟩ is _____

Answer 1

To find the unit vector in the same direction as a given vector, divide each component of the vector by its magnitude.

Step-by-step explanation:

To find the unit vector in the same direction as ⟨-3,-5⟩, we need to normalize this vector by dividing it by its magnitude. The magnitude of a vector with components ⟨x,y⟩ is given by the formula: ||v|| = √(x^2 + y^2). Therefore, the magnitude of ⟨-3,-5⟩ is ||v|| = sqrt((-3)^2 + (-5)^2) =√(9 + 25) = √(34).

Now, to find the unit vector, we divide each component of ⟨-3,-5⟩ by its magnitude: ⟨-3/√(34), -5/√(34)⟩.