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< Exercises

Analyze scalar multiplication

Vector v⃗=(x,y)\vec v=(x,y) and ∣∣v⃗∣∣=10||\vec v||= 10.
Fill in the blanks to complete the following sentences.
Vector w⃗=(15x,15y)\vec w=\left(\dfrac{1}{5}x,\dfrac{1}{5}y\right), so ∣∣w⃗∣∣=||\vec w||=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
.
Vector z⃗=(35x,35y)\vec z=\left(\dfrac{3}{5}x,\dfrac{3}{5}y\right), so ∣∣z⃗∣∣=||\vec z||=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
.
Match each vector defined above to a vector that could be its equivalent.
  • v⃗\vec v
  • w⃗\vec w
  • z⃗\vec z