Let A, B, and C Be Three Points on the Unit

question 96

Essay

Let A, B, and C be three points on the unit sphere centered at the origin whose spherical coordinates are A = (1, 0, 0), B = $\left( 1,0 , \frac { \pi } { 4 } \right)$ , and C = $\left( 1 , \frac { \pi } { 2 } , \frac { \pi } { 3 } \right)$ .(a) Find the angle between $\overrightarrow { O A }$ and $\overrightarrow { O B }$ .(b) Find the angle between $\overrightarrow { O A }$ and $\overrightarrow { O C }$ .(c) Find the angle between $\overrightarrow { O B }$ and $\overrightarrow { O C }$ .

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Definitions:

Physical Capacity

The maximum level of physiological activity that an individual can sustain, often influenced by factors like strength, endurance, and flexibility.

Stress-Induced Stamina

The capacity to endure stress while maintaining performance, which can improve with exposure to controlled levels of stress.

Reaction Time

The amount of time taken to respond to a stimulus, an indication of the speed of cognitive processing and physical response.

High-Pitched Flute

A musical instrument within the flute family that produces higher frequencies of sound, often having a bright and penetrating tone.