DP Mathematics SL Questionbank

Vector equation of a line in two and three dimensions: r=a+tbr=a+tb .
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[N/A]Directly related questions
- 18M.1.sl.TZ2.1b: The vector (2p0)⎛⎜⎝2p0⎞⎟⎠...
- 18M.1.sl.TZ2.1a: Find a vector equation for L1.
- 18M.1.sl.TZ1.9d: Point D is also on L and has coordinates (8, 4, −9). Find the area of triangle OCD.
- 18M.1.sl.TZ1.9c.ii: Write down the value of angle OBA.
- 18M.1.sl.TZ1.9c.i: Find →OB∙→AB→OB∙→AB.
- 18M.1.sl.TZ1.9b.ii: Point C (k , 12 , −k) is on L. Show that k = 14.
- 18M.1.sl.TZ1.9b.i: Find a vector equation for L.
- 18M.1.sl.TZ1.9a: Show...
- 17N.1.sl.TZ0.9c: The point D has coordinates (q2, 0, q)(q2, 0, q). Given that...
- 17N.1.sl.TZ0.9b: Find the value of pp.
- 17N.1.sl.TZ0.9a.ii: Find a vector equation for LL.
- 17N.1.sl.TZ0.9a.i: Show that...
- 17M.1.sl.TZ1.8d.ii: Hence or otherwise, find one point on L2L2 which is √5√5 units from C.
- 17M.1.sl.TZ1.8d.i: Find a unit vector in the direction of L2L2.
- 17M.1.sl.TZ1.8c: The lines L1L1 and L1L1 intersect at C(9, 13, z)C(9, 13, z). Find zz.
- 17M.1.sl.TZ1.8b: A second line L2L2, has equation r =...
- 17M.1.sl.TZ1.8a.ii: Hence, write down a vector equation for L1L1.
- 16M.2.sl.TZ2.10e: The point D lies on LL such that...
- 16M.2.sl.TZ2.10d: Given that...
- 16M.2.sl.TZ2.10c: Write down a vector equation for LL.
- 16M.2.sl.TZ2.10b: Find the coordinates of C.
- 16M.2.sl.TZ2.10a: Find →AB−−→AB.
- 16N.1.sl.TZ0.4a: Find a vector equation of the line that passes through P and Q.
- 12N.1.sl.TZ0.6a: Write down a vector equation for line L .
- 12N.1.sl.TZ0.6b: The line L intersects the x-axis at the point P. Find the x-coordinate of P.
- 12M.2.sl.TZ2.8a(i), (ii) and (iii): (i) Find →OB−−→OB . (ii) Find →OF−−→OF...
- 12M.2.sl.TZ2.8b(i) and (ii): Write down a vector equation for (i) the line OF; (ii) the line AG.
- 12M.2.sl.TZ2.8c: Find the obtuse angle between the lines OF and AG.
- 08N.1.sl.TZ0.2b: Write down an equation of the line L .
- 08N.1.sl.TZ0.2a(i) and (ii): (i) Find the velocity vector, →AB−−→AB . (ii) Find the speed of...
- 08M.2.sl.TZ1.9b: The line L1L1 has...
- 08M.2.sl.TZ1.9c(i) and (ii): The line L2L2 passes through A and is parallel to →OB−−→OB . (i) ...
- 08M.2.sl.TZ1.9d: The line L3L3 has equation...
- 12M.1.sl.TZ1.8a(i) and (ii): (i) Show that...
- 12M.1.sl.TZ1.8b: Find the cosine of the angle between →PQ−−→PQ and L2L2 .
- 12M.1.sl.TZ1.8c: The lines L1L1 and L2L2 intersect at the point R. Find the coordinates of R.
- 10N.1.sl.TZ0.8a(i), (ii) and (iii): (i) Show that...
- 10N.1.sl.TZ0.8b(i) and (ii): The line (AC) has equation r=u+sv . (i) ...
- 10N.1.sl.TZ0.8d: The lines (AC) and (BD) intersect at the point P(3, k) . Hence find the...
- 10N.1.sl.TZ0.8c: The lines (AC) and (BD) intersect at the point P(3, k) . Show that...
- 10M.1.sl.TZ1.10b: A third line L3 is perpendicular to L1 and is represented by...
- 10M.1.sl.TZ1.10a: Write down a vector equation for L2 in the form...
- 10M.1.sl.TZ1.10c: The lines L1 and L3 intersect at the point A. Find the coordinates of A.
- 10M.1.sl.TZ1.10d(i) and (ii): The lines L2and L3intersect at point C where...
- 09N.2.sl.TZ0.10b: The line L1 may be represented by...
- 09N.2.sl.TZ0.10c: The point T(−1, 5, p) lies on L1 . Find the value of...
- 09N.2.sl.TZ0.10d: The point T also lies on L2 with equation...
- 09M.1.sl.TZ2.10a: Write down the equation of L1 in the form...
- 09M.1.sl.TZ2.10b: The line L2 has equation...
- 10M.2.sl.TZ2.9a(i) and (ii): (i) Write down the coordinates of A. (ii) Find the speed of the airplane in...
- 10M.2.sl.TZ2.9b(i) and (ii): After seven seconds the airplane passes through a point B. (i) Find the coordinates of...
- 10M.2.sl.TZ2.9c: Airplane 2 passes through a point C. Its position q seconds after it passes through C is given by...
- SPNone.2.sl.TZ0.4c: Given that L1 is perpendicular to L3 , find the value of a .
- SPNone.2.sl.TZ0.4a: Write down the line that is parallel to L4 .
- SPNone.2.sl.TZ0.4b: Write down the position vector of the point of intersection of L1 and L2 .
- 11N.1.sl.TZ0.8a(i) and (ii): (i) Find →PQ . (ii) Hence write down a vector equation for...
- 11N.1.sl.TZ0.8b(i) and (ii): (i) Find the value of p . (ii) Given that L2 passes through...
- 11N.1.sl.TZ0.8c: The lines L1 and L2 intersect at the point A. Find the x-coordinate of A.
- 11M.1.sl.TZ1.2a: Write down a vector equation for L in the form...
- 11M.1.sl.TZ1.2b(i) and (ii): Find (i) →OP ; (ii) |→OP| .
- 11M.2.sl.TZ2.8d: The lines L1 and L2 intersect at point C. Find the coordinates of C.
- 11M.2.sl.TZ2.8a: Find →AB .
- 11M.2.sl.TZ2.8b: Find an equation for L1 in the form...
- 11M.2.sl.TZ2.8c: Find the angle between L1 and L2 .
- 13M.1.sl.TZ1.8b: Given that L1 is perpendicular to L2 , show that p=−6 .
- 13M.1.sl.TZ1.8a.ii: Hence, write down a vector equation for L1 .
- 14M.1.sl.TZ1.8b(i): Hence, write down a direction vector for L1;
- 14M.1.sl.TZ1.8b(ii): Hence, write down a vector equation for L1.
- 14M.1.sl.TZ1.8d(i): Write down a direction vector for L2.
- 14M.1.sl.TZ2.4c: Write down a vector equation for the line L.
- 14M.1.sl.TZ2.9a: Find the speed of Ryan’s airplane.
- 14M.1.sl.TZ2.9b: Find the height of Ryan’s airplane after two seconds.
- 15M.1.sl.TZ1.8c: The following diagram shows the line L and the origin O. The point C also lies on...
- 14N.1.sl.TZ0.10a: Write down the equation of L1.
- 14N.1.sl.TZ0.10b: A line La crosses the y-axis at a point P. Show that P has coordinates...