Find a vector of magnitude 3 in the direction of v = 10i - 24k.

Solution:

Given magnitude 3 in the direction of v = 10i - 24k.

Let the required vector be xi + yj + zk = 3 [v / |v|]

|xi + yj + zk| = √x² + y² + z² 

|10i - 24k| = √10² + (-24)² = √100 + 576 = √676 = 26

xi + yz + zk = 3(10i - 24k)/26

xi + yz + zk = = (30i - 72k) / 26

xi + yz + zk = 1.15i - 2.76k

Therefore, the required vector is 1.15i - 2.76k.

Find a vector of magnitude 3 in the direction of v = 10i - 24k.

Summary:

A vector of magnitude 3 in the direction of v = 10i - 24k is 1.15i - 2.76k.