MCV4U - Unit 8 - UNIT TEST 1. [3 Marks]. (a) Determine the vector equation of...

Transcribed Image Text:

MCV4U - Unit 8 - UNIT TEST 1. [3 Marks]. (a) Determine the vector equation of a line passing through point A(1, 4) with direction vector m = (-3, 3). (b) [3 Marks]. Determine the parametric equation of the line. 2. [Marks 6]. Determine vector and parametric equations for the line containing points E(-1, 5) and F(6, 11). 3. [Marks 6]. Determine a vector equation for the line that is perpendicular to = (4, 1) + s(3,2), s E R, and passes through point P(6, 5). 4. [10 Marks]. The parametric equation of a line are given as x = -10 - 2s, y = 8+ s, s ER, this line crosses the x-axis at point with coordinates A(a, 0) and crosses the y- axis at the point with coordinates B(0, b). If O represents the origin, determine the area of the triangle AOB. 5. [12 Marks]. A line has 7 = (1, 2) + s(2, 3), s ER, as its vector equation. On this line, the points A, B, C and D correspond to parametric values s = 0, 1, 2, and 3, respectively. Show that each of the following is true: (a) AC = 2AB (b) AD = 3AB (c) AC = AD 3 6. [4 Marks]. Are the lines 2x - 3y+ 15 = 0 and (x, y) = (1, 6) + t(6,4) parallel? Explain. 7. [4 Marks]. Determine the Cartesian equation for the line with a normal vector of (4, 5), passing through the [point A(-1, 5). MCV4U - Unit 8 - UNIT TEST 1. [3 Marks]. (a) Determine the vector equation of a line passing through point A(1, 4) with direction vector m = (-3, 3). (b) [3 Marks]. Determine the parametric equation of the line. 2. [Marks 6]. Determine vector and parametric equations for the line containing points E(-1, 5) and F(6, 11). 3. [Marks 6]. Determine a vector equation for the line that is perpendicular to = (4, 1) + s(3,2), s E R, and passes through point P(6, 5). 4. [10 Marks]. The parametric equation of a line are given as x = -10 - 2s, y = 8+ s, s ER, this line crosses the x-axis at point with coordinates A(a, 0) and crosses the y- axis at the point with coordinates B(0, b). If O represents the origin, determine the area of the triangle AOB. 5. [12 Marks]. A line has 7 = (1, 2) + s(2, 3), s ER, as its vector equation. On this line, the points A, B, C and D correspond to parametric values s = 0, 1, 2, and 3, respectively. Show that each of the following is true: (a) AC = 2AB (b) AD = 3AB (c) AC = AD 3 6. [4 Marks]. Are the lines 2x - 3y+ 15 = 0 and (x, y) = (1, 6) + t(6,4) parallel? Explain. 7. [4 Marks]. Determine the Cartesian equation for the line with a normal vector of (4, 5), passing through the [point A(-1, 5).