N-VM.B. Perform operations on vectors.

N-VM.B.4. Add and subtract vectors.

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N-VM.B.4.a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

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N-VM.B.4.b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

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N-VM.B.4.c. Understand vector subtraction $\textbf{v} - \textbf{w}$ as $\textbf{v} + (-\textbf{w})$, where $-\textbf{w}$ is the additive inverse of $\textbf{w}$, with the same magnitude as $\textbf{w}$ and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

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N-VM.B.5. Multiply a vector by a scalar.

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N-VM.B.5.a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as $c(v_x, v_y) = (cv_x, cv_y)$.

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N-VM.B.5.b. Compute the magnitude of a scalar multiple $c\textbf{v}$ using $||c\textbf{v}|| = |c|v$. Compute the direction of $c\textbf{v}$ knowing that when $|c|{v} \neq 0$, the direction of $c\textbf{v}$ is either along $\textbf{v}$ (for $c > 0$) or against $\textbf{v}$ (for $c < 0$).

• No tasks yet illustrate this standard.