Question

Calculate the length and direction of vector v = <2, 3, 1> and show that v = |v| u, where u is the direction of v.

Answer 1

The length of vector v is sqrt(14) and its direction is (2/sqrt(14), 3/sqrt(14), 1/sqrt(14)).

Step-by-step explanation:

To calculate the length (magnitude) of vector v = 2, 3, 1, we use the formula: |v| = sqrt(vx^2 + vy^2 + vz^2). Substituting the values, we get: |v| = sqrt(2^2 + 3^2 + 1^2) = sqrt(4 + 9 + 1) = sqrt(14).

To find the direction of vector v, we can normalize the vector by dividing each component by the magnitude: u = (2/sqrt(14), 3/sqrt(14), 1/sqrt(14)). Hence, the vector v = |v| u is satisfied.

Thus, the length (magnitude) of vector v is sqrt(14) and the direction of vector v is u = (2/sqrt(14), 3/sqrt(14), 1/sqrt(14)).