Practice representing vectors, finding magnitude, and performing vector operations in two dimensions.
Read each problem carefully. Show your work and include units when they are given.
Adding, subtracting, scaling, and interpreting vectors
Math - Grade 9-12
- 1
Vector a = <3, 4>. Find the magnitude of vector a.
- 2
Let u = <2, -1> and v = <5, 3>. Find u + v.
- 3
Let u = <6, 2> and v = <1, 7>. Find u - v.
- 4
Find 3< -2, 5 >.
- 5
A vector has initial point (1, 2) and terminal point (6, 8). Write the vector in component form.
- 6
A plane travels 120 km east and then 50 km north. Represent the trip as a vector in component form.
- 7
Find the magnitude of v = <8, 15>.
- 8
Let p = <-4, 9> and q = <3, -2>. Find 2p + q.
- 9
Determine whether the vectors <4, 6> and <2, 3> are scalar multiples of each other. Explain briefly.
- 10
Find the midpoint of the segment with endpoints A(2, -3) and B(10, 5).
- 11
A hiker walks 7 miles west and 24 miles south. Write the displacement vector in component form and find its magnitude.
- 12
Let a = <1, 2> and b = <-3, 4>. Find a + 2b.
- 13
A vector has magnitude 10 and points directly along the positive x-axis. Write the vector in component form.
- 14
Find the distance between the points ( -1, 4 ) and ( 5, -4 ).
- 15
Vector u = <x, 7> and vector v = <3, 2>. If u + v = <11, 9>, find x.