Question

The direction cosines of the \( z \)-axis are:

• A. \( (1, 0, 1) \)
• B. \( (0, 0, 1) \)
• C. \( (0, 1, 0) \)
• D. \( (0, 0, 0) \)

Hint:

Direction cosines of a vector are always the cosines of the angles it makes with the coordinate axes. For the coordinate axes themselves: - \( x \)-axis: \( (1,0,0) \) - \( y \)-axis: \( (0,1,0) \) - \( z \)-axis: \( (0,0,1) \)

Answer 1

The Correct Option is B

Step 1: Direction cosines are the cosines of the angles that a vector makes with the \( x \)-, \( y \)-, and \( z \)-axes. Step 2: The \( z \)-axis is the line along the \( z \)-direction, so: - Angle with \( x \)-axis = 90°, \( \cos 90^\circ = 0 \) - Angle with \( y \)-axis = 90°, \( \cos 90^\circ = 0 \) - Angle with \( z \)-axis = 0°, \( \cos 0^\circ = 1 \) Therefore, direction cosines are \( (0, 0, 1) \). Final Answer: \( \boxed{(0, 0, 1)} \)