Precalculus Vectors in the Plane Quiz: 10 Questions with Explanations

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This vectors quiz for Precalculus covers vectors in the plane (Common Core N-VM.A.1, N-VM.A.2, N-VM.A.3, N-VM.B.4, N-VM.B.5), with a free PDF to print.

Pick the best answer for 10 questions on vectors in the plane. Explanations name typical mistakes, such as adding magnitudes instead of components.

Precalculus · Common Core State Standards: N-VM.A.1, N-VM.A.2, N-VM.A.3, N-VM.B.4, N-VM.B.5

Vectors quiz: 10 questions

Question 1
What is the magnitude of \(\langle3,-4\rangle\)?

Question 2
Find \(\langle2,5\rangle+\langle-3,1\rangle\).

Question 3
What is \(3\langle1,-2\rangle\)?

Question 4
What is the dot product \(\langle1,4\rangle\cdot\langle2,-3\rangle\)?

Question 5
The figure shows head-to-tail addition. Which is the sum?

-2-112345-3-2-112345xyuvu + v
Vectors u, v and their sum.

Question 6
What is the unit vector in the direction of \(\langle0,-7\rangle\)?

Question 7
If \(\vec{u}\cdot\vec{v}=0\) for nonzero vectors, the vectors are…

Question 8
A 30 N force east and a 40 N force north act together (see the figure). What is the resultant magnitude?

-112345-112345xy30 N40 N50 N
Resultant of two forces.

Question 9
What is the vector from \(P(1,2)\) to \(Q(4,6)\)?

Question 10
A boat crosses a river heading straight across at 6 mph with a current of 2.5 mph (see the figure). What is its speed?

-2-112345-11234567xy6 mph2.5 mph6.5 mph
Boat and current.

Remember

Remember
  • Vector from P to Q: ⟨x2 – x1, y2 – y1⟩; magnitude sqrt(a^2 + b^2).
  • Components of magnitude r at angle theta: .
  • Unit vector in the direction of v: v divided by |v|.
  • Dot product: ⟨a, b⟩ . ⟨c, d⟩ = ac + bd; zero means perpendicular.
  • Resultant force or velocity is the vector sum of the parts.

How to use this vectors quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the vectors quiz as a PDF with the button below and keep it with your notes.

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Precalculus Vectors in the Plane Quiz: 10 Questions with Explanations

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