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

Vectors are very interesting concepts in mathematics that have an immense number of applications in engineering and physics.

## Answer: A vector with the same direction as (−4, 4, 6) having Length as 6 is (−12/√17, 12/√17, 18/√17).

Let's understand the solution in detail.

**Explanation:**

Given: Let A_{0} = (−4, 4, 6).

Let A_{1} be the vector in the same direction as A_{0} but with a length of 6 as shown below

⇒ A_{1} = (−4u, 4u, 6u)

The length of a vector with coordinates (−4u, 4u, 6u) is equal to

√(16u^{2} + 16u^{2} + 36u^{2}) = u√68

Given that the length of this vector should be 6

Thus,

⇒ u√68 = 6

⇒ u = 6 / √68

⇒ u = 6 / 2√17

⇒ u = 3/√17

Substituting the value of 'u' back to A_{1} = (−4u, 4u, 6u)

A_{1} = (−4 × 3/√17, 4 × 3/√17, 6 × 3/√17)

A_{1} = (−12/√17, 12/√17, 18/√17)