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Boats
A and
B are participating in a race. Their velocities are represented by vectors
vec(a) and
vec(b), respectively.
Which option best describes the meaning of the following statement?

vec(a)= vec(b)
Choose 1 answer:
(A) The two boats move at the same speed and in the same direction.
(B) The two boats move at the same speed, but not necessarily in the same direction.
(C) The two boats move in the same direction, but not necessarily at the same speed.

Boats $A$ and $B$ are participating in a race. Their velocities are represented by vectors $\vec{a}$ and $\vec{b}$ , respectively. $\newline$ Which option best describes the meaning of the following statement? $\newline$ $\vec{a}=\vec{b}$ $\newline$ Choose $1$ answer: $\newline$ (A) The two boats move at the same speed and in the same direction. $\newline$ (B) The two boats move at the same speed, but not necessarily in the same direction. $\newline$ (C) The two boats move in the same direction, but not necessarily at the same speed.

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Simplify expressions involving rational exponents

Full solution

Q. Boats

A

and

B

are participating in a race. Their velocities are represented by vectors

\vec{a}

and

\vec{b}

, respectively.

\newline

Which option best describes the meaning of the following statement?

\newline

\vec{a}=\vec{b}

\newline

Choose

1

answer:

\newline

(A) The two boats move at the same speed and in the same direction.

\newline

(B) The two boats move at the same speed, but not necessarily in the same direction.

\newline

(C) The two boats move in the same direction, but not necessarily at the same speed.

Definition of Equal Vectors: When we say that two vectors are equal, $\vec{a} = \vec{b}$ , it means that both the magnitude and the direction of the two vectors are the same. In the context of velocity vectors, this implies that both the speed (magnitude of velocity) and the direction of motion are identical for both boats.
Option (A): Option (A) states that the two boats move at the same speed and in the same direction. This is consistent with the definition of equal vectors, as both the magnitude (speed) and direction must be the same for $\vec{a}$ to equal $\vec{b}$ .
Option (B): Option (B) suggests that the boats move at the same speed but not necessarily in the same direction. This is incorrect because if the directions were different, the vectors would not be equal.
Option (C): Option (C) suggests that the boats move in the same direction but not necessarily at the same speed. This is also incorrect because if the speeds were different, the magnitudes of the vectors would not be equal, and thus the vectors themselves would not be equal.

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