Fast

for v=-5i-2j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vectors i and j

The unit vector u is (-5/√29) i - (2/√29) j

Step-by-step explanation:

* Lets revise the meaning of unit vector

- The unit vector is the vector ÷ the magnitude of the vector

- If the vector w = xi + yj

- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w

- The unit vector u in the direction of w is u = w/IwI

- The unit vector u = (xi + yj)/√(x² + y²)

- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j

* Now lets solve the problem

∵ v = -5i - 2j

∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29

- The unit vector u = v/IvI

∴ u = (-5i - 2j)/√29 ⇒ spilt the terms

∴ u = (-5/√29) i - (2/√29) j

* The unit vector u is (-5/√29) i - (2/√29) j

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