Question

Find a vector of magnitude 3 in the direction of v=24i-18k

Answer 1

`\vec u = (12\cdot √(30))/(5)\,\hat{i}-(9\cdot √(30))/(5) \,\hat{k}`

Explanation:

Vectors are represented by magnitude and direction, which is equivalent to the unit vector multiplied by a given magnitude:

`\vec u = r\cdot (\vec v)/(\|\vec v\|)`

The magnitude of
`\vec v` is given by Pythagorean Theorem. If
`\vec v = 24\,\hat {i}-18\,\hat{k}`, then:

`\|\vec v\|=\sqrt{24^(2)+(-18)^(2)}`

`\|\vec v\| = √(30)`

If
`r = 3`,
`\vec v = 24\,\hat {i}-18\,\hat{k}` and
`\|\vec v\| = √(30)`, then:

`\vec u = (72)/(√(30))\,\hat{i}-(54)/(√(30)) \,\hat{k}`

`\vec u = (12\cdot √(30))/(5)\,\hat{i}-(9\cdot √(30))/(5) \,\hat{k}`