Calculus questions

Question

1. Find a unit vector that has the same direction as the given vector.

−5i + 7j

2.

Find a unit vector that has the same direction as the given vector.

8i - j + 5k

Answer 1

To find a unit vector that is in the same direction as a given vector, multiply the given vector by 1 over its magnitude.

So, for the vector -5i + 7j, the magnitude is √[(-5)²+7²] = √74

Unit vector: (-5/√74) i + (7/√74) j

Do the other problem in a similar manner.