Multiply a vector by a scalar.
Number and Quantity
Vector & Matrix Quantities: Perform operations on vectors.
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Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as 𝑐(𝑣ₓ, 𝑣 subscript 𝑦) = (𝑐𝑣ₓ, 𝑐𝑣 subscript 𝑦).
Compute 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).