Lesson Worksheet: The Angle between Two Vectors in the Coordinate Plane Mathematics • 12th Grade

In this worksheet, we will practice using the dot product to find the angle between two nonzero vectors in a plane.

Q1:

If ||=10A and ||=17B, where the measure of the angle between A and B is 120โˆ˜, find (+)โ‹…(โˆ’2)ABAB correct to the nearest hundredth.

Q2:

Suppose ๐ด๐ต๐ถ๐ท is a square of side 47. Determine ๏ƒ ๐ด๐ตโ‹…๏ƒ ๐ด๐ถ.

Q3:

Suppose a rectangle ๐ด๐ต๐ถ๐ท with ๐ด๐ต=32 and ๐ต๐ถ=11. Determine ๏ƒ ๐ด๐ถโ‹…๏ƒ ๐ต๐ท.

Q4:

Find the value of ๐œƒ approximated to the nearest hundredth.

Q5:

ABโ‹…=.

  • A||||AB
  • B||+||AB
  • C||||๐œƒABtan
  • D||||๐œƒABcos
  • E||||๐œƒABsin

Q6:

If A and B satisfy ABโ‹…=0, how are the two vectors related?

  • Aperpendicular
  • Bparallel

Q7:

Consider a square ๐ด๐ต๐ถ๐ท of side 32.6. Determine ๏ƒ ๐ด๐ทโ‹…๏ƒ ๐ด๐ถ.

Q8:

In a rectangle ๐ด๐ต๐ถ๐ท, ๐ด๐ต=7.7 and ๐ต๐ถ=3.8. Determine ๏€บ5๏ƒ ๐ด๐ต๏†โ‹…๏€บ๏ƒ ๐ด๐ถ๏†.

Q9:

If ๐ด๐ต๐ถ๐ท๐ธ๐น is a regular hexagon whose side is 7.1, find ๏€บ๏ƒ ๐ถ๐ด+๏ƒ ๐ด๐น๏†โ‹…๏ƒ ๐ด๐ท.

Q10:

If ๐ด๐ต๐ถ๐ท๐ธ๐น is a regular hexagon whose side is 9.6, find ๏€บ๏ƒ ๐ด๐ตโˆ’๏ƒŸ๐ธ๐น๏†โ‹…๏ƒ ๐ด๐ท.

This lesson includes 24 additional questions and 207 additional question variations for subscribers.

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