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Vectors in the Plane and Three-Space- HW Problems
Sketch the vectors 𝑣⃗ , 𝑤
⃗⃗⃗, 𝑣⃗ + 𝑤
⃗⃗⃗ , and 𝑣⃗ − 𝑤
⃗⃗⃗ .
1. 𝑣⃗ =< 2, −3 > , 𝑤
⃗⃗⃗ =< −1, 5 >
2. 𝑣⃗ =< 1, −2, 4 > , 𝑤
⃗⃗⃗ =< 3, 3, −2 >
Write a vector equation and parametric equations of a line through the
following points.
3. (2, −3), (−1,5)
4. (1, −2, 4), (3, 3, −2)
5. Find a vector equation and parametric equations of a line through
the point (2, −3, 1) in the direction of 𝑣⃗ =< 4, 1, −2 >.
6. Find the points of intersection of the line given by
𝑥 = 4 − 2𝑡, 𝑦 = −2 + 4𝑡, 𝑧 = 9 + 3𝑡
with the 3 coordinate planes.
7. Write a vector equation of the line segment from (−1, 2, 4) to
(4, 3, −2).
Vectors in the Plane and Three-Space- HW Problems
Sketch the vectors 𝑣⃗ , 𝑤
⃗⃗⃗, 𝑣⃗ + 𝑤
⃗⃗⃗ , and 𝑣⃗ − 𝑤
⃗⃗⃗ .
1. 𝑣⃗ =< 2, −3 > , 𝑤
⃗⃗⃗ =< −1, 5 >
2. 𝑣⃗ =< 1, −2, 4 > , 𝑤
⃗⃗⃗ =< 3, 3, −2 >
Write a vector equation and parametric equations of a line through the
following points.
3. (2, −3), (−1,5)
4. (1, −2, 4), (3, 3, −2)
5. Find a vector equation and parametric equations of a line through
the point (2, −3, 1) in the direction of 𝑣⃗ =< 4, 1, −2 >.
6. Find the points of intersection of the line given by
𝑥 = 4 − 2𝑡, 𝑦 = −2 + 4𝑡, 𝑧 = 9 + 3𝑡
with the 3 coordinate planes.
7. Write a vector equation of the line segment from (−1, 2, 4) to
(4, 3, −2).
