Find a unit vector that has the same direction as the given vector 8i - j + 4k?

Solution:

Given vector 8i - j + 4k

The unit vector for a vector xi + yj + zk is given xi + yj + zk / |xi + yj + zk|

Here x = 8, y = -1, z = 4

Unit vector U = 8i - j + 4k / |8i - j + 4k|

Modulus of a vector is √{x² +y² +z²},

|8i - j + 4k| = √ {8² + (-1)² +4²}

= √{64 +1 +16}

= √81

|8i - j + 4k| = 9

U = {8i - j + 4k }/9

U = 8i/9 - j/9 + 4k/9

The unit vector is 8i/9 - j/9 + 4k/9

Find a unit vector that has the same direction as the given vector 8i - j + 4k?

Summary:

A unit vector that has the same direction as the given vector 8i - j + 4k is 8i/9 - j/9 + 4k/9.