MCV4U, CALCULUS AND VECTORS TEST Chapter 6 ... - La Citadelle

MCV4U, CALCULUS AND VECTORSTEST Chapter 6PLANESTeacher: Teodoru GugoiuDate……………………..............Name ……………………..............=251. Find the distance between the parallel planes. [K/U 2 marks]π : x + y − z + 1 0 , π : −3x− 3y+ 3z− 4 01 =2 =2. Find the intersection with the coordinate axes for the plane π : x − 2y+ 3z+ 6 = 0 . [K/U 2 marks]3. Consider the plane determined by the following vector equation: [K/U 2 marks]r= ( −2,−1,0)+ t(−1,0,1)+ s(0,1,2)a) Identify the direction vectors.b) Find two points on this plane.Page 1 of 4

4. Convert each equation of a plane to vector and scalar forms. [K/U 2 marks]⎧x= 1+t + s⎪⎨y= −1−s⎪⎩z= 2 − t − 2s5. Find the vector equation of a plane passing through the points A(−1,0,1) and B (0,1,2 ) and C ( 1, −1,0).[A 2 marks]6. For each case, find the distance between the given plane and the given point. [A 2 marks]x − 2 y + 3z−12= 0 , B ( 1, −2,1)Page 2 of 4

7. Find the intersection between the given line and the given plane. [A 4 marks]π : 2x− y + 3z+ 6 = 0 , L : r = (0,1,3) + t(1,−2,3)8. Find the equation of the line of intersection for each pair of planes (if it exists). [A 4 marks]π : x − y + z − 2 0 , π : 2x− 3y+ 4z−1201 =2 =Page 3 of 4

9. Solve the following system of equations. Give a geometric interpretation of the result. [A 5 marks]⎧2x+ y + 6z− 7 = 0⎪⎨3x+ 4y+ 3z+ 8 = 0⎪⎩x− 2y− 4z− 9 = 0Page 4 of 4