Question

Find a vector v parallel to u = 5i + 7j - 5k and with magnitude = 6.

Answer 1

To find a vector parallel to u = 5i + 7j - 5k with a magnitude of 6, divide the components of u by its magnitude to find the unit vector, and then multiply the unit vector by 6 to find the desired vector.

Step-by-step explanation:

To find a vector parallel to u = 5i + 7j - 5k with a magnitude of 6, we first need to find the unit vector in the direction of u. The unit vector, denoted as û, is calculated by dividing u by its magnitude:

û = u/|u|

Then, we can multiply û by 6 to get a vector parallel to u with a magnitude of 6:

v = 6û

Let's calculate:

1. Calculate the magnitude of u using the formula: |u| = sqrt(5^2 + 7^2 + (-5)^2)
2. Divide each component of u by |u| to find û
3. Multiply each component of û by 6 to find v

Using this method, the vector v parallel to u and with magnitude 6 would be:

v = 6(5/|u|)i + 6(7/|u|)j + 6(-5/|u|)k