Answer: All three expressions are equivalent.
- A |-3| / (sqrt(14)*sqrt(6)), using only the absolute value
- B 3 / (sqrt(14)*sqrt(6)), dropping the negative sign
- C (2-3-2) / (sqrt(14)*sqrt(6)), an unsimplified numerator
- D All three expressions are equivalent
Correct answer: D. All three expressions are equivalent
Explanation: n<sub>1</sub>=(2,3,-1), n<sub>2</sub>=(1,-1,2). n<sub>1</sub>.n<sub>2</sub>=2-3-2=-3. |n<sub>1</sub>|=sqrt(14), |n<sub>2</sub>|=sqrt(6). cos(theta)=|n<sub>1</sub>.n<sub>2</sub>|/(|n<sub>1</sub>||n<sub>2</sub>|) = |-3|/sqrt(84) = 3/sqrt(84). Options A, B, C all equal the same value.
Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.
Concept context
Lines and planes in 3D space, direction cosines, distances, and angles