Which of the following vectors are equal to n d if M=(2,1) and N=(3,-4) ? (a) AB, where A=(1,-1)

step 1 to 1A, 2B, 3C, and v is equal to negative 4A, B, negative 2C. So U plus V, and we're going to ad

Which of the following vectors are equal to n d if M=(2,1)...

Which of the following vectors are equal to $\overrightarrow{n d}$ if $M=(2,1)$ and $N=(3,-4)$ ? (a) $\overrightarrow{\mathrm{AB}}$, where $\mathrm{A}=(1,-1)$ and $\mathrm{B}=(2,3)$ (b) $\mathrm{CD}$, where $\mathrm{C}=(-4,5)$ and $\mathrm{D}=(-3,10)$ (c) $\mathrm{EF}$, where $E=(3,-2)$ and $F=(4,-7)$.

Which of the following vectors are equal to $\overrightarrow{n d}$ if $M=(2,1)$ and $N=(3,-4)$ ?
(a) $\overrightarrow{\mathrm{AB}}$, where $\mathrm{A}=(1,-1)$ and $\mathrm{B}=(2,3)$
(b) $\mathrm{CD}$, where $\mathrm{C}=(-4,5)$ and $\mathrm{D}=(-3,10)$
(c) $\mathrm{EF}$, where $E=(3,-2)$ and $F=(4,-7)$.

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Key Concepts

Vector Subtraction

Vector subtraction is a fundamental operation where the coordinates of one point are subtracted from the coordinates of another to yield a new vector. This method is used to compute displacement vectors and to check if two vectors are equivalent by comparing their resulting components.

Vector Equality

Two vectors are considered equal if they have the same magnitude and direction, which is determined by comparing their corresponding components. The location of the vector in space is not as important as having identical component values when establishing equality.

Displacement Vector

A displacement vector is obtained by subtracting the coordinates of the starting point from the coordinates of the ending point. This process provides a vector that represents the change in position, capturing both magnitude and direction, which is crucial for comparing vectors in geometric problems.

Vector Components

Vector components refer to the representation of a vector in terms of its individual coordinate differences (for instance, the change in the x-coordinate and the change in the y-coordinate in 2D space). This breakdown allows us to analyze vectors by comparing these components directly.

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