# Find a vector that has the same direction as −2, 4, 6 but has length 6.

## Answer: The vector with direction as <-2, 4, 6> and length 6 is given as 3<-2, 4, 6> / sqrt(14).

**Explanation:**

Let u be the unit vector in same direction as v = <-2, 4, 6>

Then, u = v / |v| = <-2, 4, 6> / sqrt[(-2)^{2} + (4)^{2} + (6)^{2]}

u = <-2, 4, 6> / sqrt(56)

u = <-2, 4, 6> / 2sqrt(14)

Now let w be the vector with length 6 and in same direction as v

Since |u| = 1, so w = 6 |u|

So, w = 6 <-2, 4, 6> / 2sqrt(14)

w = 3<-2, 4, 6> / sqrt(14)