Question

A vector v is in the direction of the vector 8i-6j and has magnitude 5. Find v in the form ai+bj

Answer 1

To find vector v with a magnitude of 5 in the direction of 8i-6j, first calculate the unit vector (0.8i - 0.6j) and then multiply by 5 to get v = 4i - 3j.

Step-by-step explanation:

To find a vector v that is in the direction of the vector 8i-6j and has a magnitude of 5, we first need to determine the unit vector in the direction of 8i-6j. This is done by dividing the vector by its magnitude. The magnitude of 8i-6j is calculated using the Pythagorean theorem: |8i-6j| = √(8^2 + (-6)^2) = √(64 + 36) = √100 = 10. Therefore, the unit vector is (8i-6j)/10 = 0.8i - 0.6j.

Now we can find vector v by multiplying the unit vector by the desired magnitude, which is 5 in this case: v = 5 * (0.8i - 0.6j) = (5 * 0.8)i + (5 * -0.6)j = 4i - 3j.

Answer 2

4i - 3j.

Step-by-step explanation:

The slope of 8i - 6j = -6/8 = = -3/4 and the magnitude is √(8^2 + 6^2) = 10

So the required vector is 4i - 3j ( with slope -3/4 and magnitude √(9+16) = 5).