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Vectors: Direction, Unit Vectors & Angles — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Give exact answers. Write vectors as <a, b> and angles in degrees (0° ≤ θ < 360° for direction angles).
How to solve
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Example
u = <0, -1> and v = <-5, 1>. Find 3u - v.
Answer: <5, -4>
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <-4, -4> and v = <-1, 0>. Find 4u - v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <1, -2> and v = <0, -5>. Find 2u - 2v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <4, 2> and v = <-5, -4>. Find 3u - 3v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <4, 1> and v = <-1, -5>. Find 3u + 3v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <1, -3> and v = <-1, 3>. Find 4u - v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <1, 5> and v = <-3, -3>. Find 4u + 2v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <4, 4> and v = <-4, -5>. Find 2u + v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <2, 2> and v = <1, -1>. Find 3u - 3v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Vectors: Direction, Unit Vectors & Angles — Easy Worksheet 2
Give exact answers. Write vectors as <a, b> and angles in degrees (0° ≤ θ < 360° for direction angles).