MCV 4U Unit 3 Test: Vectors and it’s applications
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
MCV 4U
Unit 3 Test: Vectors and it’s applications
1. Find the direction vector of the symmetric equation of 
in 2D [1K]
2. Justify if the point (4,2) is on the line L:
= (−2,7) + t(1, −1) [1A1T]
3. Find the parametric, vector, symmetric equations for the line through the points (3, -2, 3), and (4, 4, 6) [2K1A1T+1C]
4. Determine vector equations and cartesian equation of the plane containing the points A(3 ,-2 ,3) B(4, 4, 6) and a vector 
= [2, 1,0] [2A2T+1C]
5. Calculate the following using these vectors: [+4C]
6. A boat wishes to cross a river from point A to a point B directly across the river where the pathis perpendicular to the shore. The width of the river is 100m. The boat can travel at a speed of 12m/s relative to the water and the river is flowing at 3m/s [W].
a) Draw a diagram to describe the situation. [1A1C]
b) Determine the direction that the boat should go so that it ends its journey at point B. [1A1T]
c) Determine the speed of the boat relative to the shore. [1A1T]
7. Is the following expression 
a vector, a scalar, or meaningless? Explain in English. [1A3C]
8. An object is hanging from two ropes. One has a tension of 200 N and makes an angle of 40° with the ceiling. The other rope makes an angle of 30° with the ceiling. Calculate the downward force cause by the mass of the object [1A3T1C]
9. Find the intersection for the following line with the coordinate axes and planes [x, y, z] = [3, -2, −3] + t[4, 4, −6] [2A2T1C]
10. Determine the situation of the following two lines, and find a vector equation of the plane that includes these two lines [2A2T2C]
Formulas:
2024-01-03