Precalculus Vectors in the Plane Test with Point Values (PDF)
This vectors test 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.
Time and points
- Grade: Precalculus
- Chapter: Vectors in the Plane
- Standards: N-VM.A.1, N-VM.A.2, N-VM.A.3, N-VM.B.4, N-VM.B.5
- Time: 45 minutes
- Total: 20 points
Vectors test: questions
Question 1 – Component form and magnitude [2 pts]
Find the component form and magnitude of the vector from \(P(-3,4)\) to \(Q(2,-8)\).
Question 2 – Magnitude and direction [2 pts]
Find the magnitude and direction angle of \(\langle-5,5\rangle\).
Question 3 – Vector arithmetic [2 pts]
Let \(\vec{u}=\langle4,-1\rangle\) and \(\vec{v}=\langle-2,3\rangle\). Find \(2\vec{u}-3\vec{v}\).
Question 4 – Unit vector [2 pts]
Find the unit vector in the direction of \(\langle-5,12\rangle\).
Question 5 – Sum of two vectors [3 pts]
The vectors \(\vec{u}\) and \(\vec{v}\) are shown. (a) Write each in component form. (b) Find \(\vec{u}+\vec{v}\). (c) Find \(|\vec{u}+\vec{v}|\) to the nearest hundredth.
Question 6 – Perpendicular vectors [2 pts]
Find \(k\) so that \(\langle3,k\rangle\) and \(\langle4,-6\rangle\) are perpendicular.
Question 7 – Angle between vectors [2 pts]
Find the angle between \(\langle2,3\rangle\) and \(\langle-1,4\rangle\) to the nearest hundredth of a degree.
Question 8 – Airplane and wind [3 pts]
A plane flies due east at \(300\) mph relative to the air. A wind blows toward the south at \(50\) mph. (a) Write the ground velocity in component form. (b) Find the ground speed to the nearest tenth. (c) Find the angle south of east of its path to the nearest tenth.
Question 9 – Work [2 pts]
A force \(\langle20,15\rangle\) N moves an object along \(\langle4,3\rangle\) m. Find the work \(W=\vec{F}\cdot\vec{d}\).
Key facts behind this vectors test
- 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 test
Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.
All Precalculus chapters: Precalculus math.
