Question

refer to the vectors m through t at the right. name all groups of vectors that appear to be equal. choose the correct answer below. a. n and r; m, p, and t b. m, o, p and q; n, r, and s c. m and p; n and r d. m and p; p and q; m and q; n and r; n and s; s and r

Explanation:

Step1: Recall the definition of equal vectors

Equal vectors have the same magnitude and direction.

Step2: Analyze each option

• Option A: Vectors \(m\), \(p\), \(t\) do not have the same direction. Vectors \(n\) and \(r\) have the same direction but \(m\), \(p\), \(t\) are not a valid group of equal vectors.
• Option B: Vectors \(m\) and \(o\) do not have the same direction. Vectors \(n\), \(r\), \(s\) - \(s\) has a different direction from \(n\) and \(r\) (opposite direction in terms of the vertical - like orientation).
• Option C:
• For vectors \(m\) and \(p\): They have the same direction (parallel) and appear to have the same length.
• For vectors \(n\) and \(r\): They have the same direction (parallel) and appear to have the same length.
• Option D: Vectors \(n\) and \(s\) have opposite directions (one is upwards, one is downwards in the vertical - like orientation), so they are not equal.

Answer:

C. \(m\) and \(p\); \(n\) and \(r\)