Given the vector a=<9,10,90>
Find the unit vector in the same direction in component form
it's just a/|a| = <9/91, 10/91, 90/91>
To find the unit vector in the same direction as a given vector, you need to divide each component of the vector by its magnitude.
To get the magnitude of a vector, you can use the formula:
|a| = sqrt(a₁² + a₂² + a₃²)
= sqrt(9² + 10² + 90²)
= sqrt(81 + 100 + 8100)
= sqrt(8281)
= 91
Now, divide each component of the vector by its magnitude to find the unit vector:
Unit vector a = (9/|a|, 10/|a|, 90/|a|)
= (9/91, 10/91, 90/91)
Therefore, the unit vector in the same direction as vector a in component form is (9/91, 10/91, 90/91).