Any vector can be written as a unit vector multiplied by the magnitude of the vector (a positive scalar). Write each of the following vectors as the magnitude of the vector times the appropriate unit vector:
< 0.00330, 0, -0.00330 >
To write the vector < 0.00330, 0, -0.00330 > as the magnitude of the vector times the appropriate unit vector, we need to find the magnitude of the vector and then divide each component by the magnitude to obtain the unit vector.
The magnitude of a vector (represented as ||v||) can be calculated using the formula:
||v|| = sqrt(v1^2 + v2^2 + v3^2)
For the given vector < 0.00330, 0, -0.00330 >, the magnitude can be calculated as follows:
||v|| = sqrt((0.00330)^2 + 0^2 + (-0.00330)^2)
= sqrt(0.00001089 + 0 + 0.00001089)
= sqrt(0.00002178)
≈ 0.00466
Once we have the magnitude, we can find the unit vector by dividing each component of the vector by the magnitude. So the unit vector u would be:
u = < v1/||v||, v2/||v||, v3/||v|| >
= < 0.00330/0.00466, 0/0.00466, -0.00330/0.00466 >
= < 0.708, 0, -0.708 >
Therefore, the vector < 0.00330, 0, -0.00330 > can be written as:
0.00466 * < 0.708, 0, -0.708 >