A unit vector in the same direction as v can be found by dividing v by its magnitude.

Step 1: Calculate the magnitude (or length) of v. The magnitude of a vector v = ⟨a, b⟩ is given by √(a² + b²).

For v = ⟨8, 1⟩, the magnitude is √(8² + 1²) = √(64 + 1) = √65.

Step 2: Divide each component of v by the magnitude to get the unit vector.

The unit vector in the direction of v = ⟨8, 1⟩ is then ⟨8/√65, 1/√65⟩.

Question

A unit vector in the same direction as v can be found by dividing v by its magnitude.

Step 1: Calculate the magnitude (or length) of v. The magnitude of a vector v = ⟨a, b⟩ is given by √(a² + b²).

For v = ⟨8, 1⟩, the magnitude is √(8² + 1²) = √(64 + 1) = √65.

Step 2: Divide each component of v by the magnitude to get the unit vector.

The unit vector in the direction of v = ⟨8, 1⟩ is then ⟨8/√65, 1/√65⟩.

Knowee AI · Accepted Answer

A unit vector in the same direction as v can be found by dividing v by its magnitude.

Step 1: Calculate the magnitude (or length) of v. The magnitude of a vector v = ⟨a, b⟩ is given by √(a² + b²).

For v = ⟨8, 1⟩, the magnitude is √(8² + 1²) = √(64 + 1) = √65.

Step 2: Divide each component of v by the magnitude to get the unit vector.

The unit vector in the direction of v = ⟨8, 1⟩ is then ⟨8/√65, 1/√65⟩.

Given the following vector v:v=⟨8,1⟩𝑣=⟨8,1⟩Step 1 of 2 : Find a unit vector pointing in the same direction as v.