N.VM.B: Perform operations on vectors.

Perform operations on vectors.

N.VM.B.4Add and subtract vectors.N.VM.B.4.aAdd 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.N.VM.B.4.bGiven two vectors in magnitude and direction form, determine the magnitude and direction of their sum.N.VM.B.4.cUnderstand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as 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.N.VM.B.5Multiply a vector by a scalar.N.VM.B.5.aRepresent 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).N.VM.B.5.bCompute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).N.VM.B.5.cDetermine the dot product of two vectors.

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