Question

Find unit vector parallel to \(- (s + 4s) \hat{i} + (7 - 2s) \hat{j} + (3 + 4s) \hat{k}\)

Hint:

To find a unit vector, first compute the vector's magnitude and then divide each component by the magnitude.

Answer 1

Step 1: Simplify the vector expression.
First, simplify the vector components: \[ - (s + 4s) \hat{i} = -5s \hat{i}, \quad (7 - 2s) \hat{j}, \quad (3 + 4s) \hat{k} \] So, the vector is: \[ \mathbf{V} = -5s \hat{i} + (7 - 2s) \hat{j} + (3 + 4s) \hat{k} \]
Step 2: Find the magnitude of the vector.
The magnitude of the vector is given by: \[ |\mathbf{V}| = \sqrt{(-5s)^2 + (7 - 2s)^2 + (3 + 4s)^2} \]
Step 3: Calculate the unit vector.
The unit vector \(\hat{v}\) parallel to \(\mathbf{V}\) is obtained by dividing the vector by its magnitude: \[ \hat{v} = \frac{\mathbf{V}}{|\mathbf{V}|} \]