DP Mathematics HL Questionbank

• Syllabus

4.3

Sub sections and their related questions

Vector equation of a line in two and three dimensions: \(r = a + \lambda b\) .

• 12M.2.hl.TZ1.4: The planes \(2x + 3y - z = 5\) and \(x - y + 2z = k\) intersect in the line...
• 12M.2.hl.TZ1.13d: Find the vector equation of L , the line of intersection of \({\Pi _1}\) and \({\Pi _2}\) , and...
• 12M.2.hl.TZ1.13e: A methane molecule consists of a carbon atom with four hydrogen atoms symmetrically placed around...
• 12M.2.hl.TZ2.11b: Given that the system of equations can be solved, find the solutions in the form of a vector...
• 12N.2.hl.TZ0.13b: The planes \({\pi _1}\) and \({\pi _2}\) intersect in the line \({L_1}\) . Show that the vector...
• 11M.2.hl.TZ2.11e: Write down the vector equation of the line through the origin (0, 0, 0) that is perpendicular to...
• 11M.2.hl.TZ2.11f: Hence find the point on the plane that is closest to the origin.
• SPNone.2.hl.TZ0.10b: (i)     Find the vector equation of the line \({L_1}\) containing the points A and B. (ii)    ...
• 13M.2.hl.TZ1.11a: Find a vector equation for the line, \({L_1}\), which passes through the points P and Q. The...
• 13M.2.hl.TZ1.11c: Find the acute angle between \({L_1}\) and \({L_2}\).
• 13M.2.hl.TZ1.11d: Let S be a point on \({L_2}\) such that...
• 13M.2.hl.TZ1.11e: Let S be a point on \({L_2}\) such that...
• 13M.1.hl.TZ2.11d: Find a vector equation of (AB).
• 13M.1.hl.TZ2.11e: The point D on (AB) is such that \(\overrightarrow {{\text{OD}}} \) is perpendicular to...
• 11N.2.hl.TZ0.13a: Find the vector equation of L, the line of intersection of \({\Pi _1}\) and \({\Pi _2}\).
• 09N.2.hl.TZ0.2: The vector equation of line \(l\) is given as...
• 09N.2.hl.TZ0.11: (a)     Find the coordinates of the point \(A\) on \({l_1}\) and the point \(B\) on \({l_2}\)...
• 14M.1.hl.TZ1.12d: Find a vector equation of the line \(L\), through M, perpendicular to the plane \({\mathit{\Pi }}\).
• 14M.1.hl.TZ2.12a: Given the points A(1, 0, 4), B(2, 3, −1) and C(0, 1, − 2) , find the vector equation of the line...
• 13N.1.hl.TZ0.11d: A second plane \({\Pi _2}\) is defined by the Cartesian equation \({\Pi _2}:4x - y - z = 4\)....
• 13N.2.hl.TZ0.9: A line \({L_1}\) has equation r =...
• 14N.2.hl.TZ0.5a: Find the Cartesian equation of \(\pi \).
• 15M.2.hl.TZ2.13a: Show that the lines \({L_1}\) and \({L_2}\) are skew.
• 15N.1.hl.TZ0.13b: (i)     Find a vector equation of the line that passes through \(B\) and \(R\) in terms of...
• 15N.1.hl.TZ0.13c: Show that the line segment [\(CP\)] also includes the point \(G\).
• 15N.2.hl.TZ0.10a: find the vectors \({{a}}\) and \({{b}}\).
• 16M.1.hl.TZ2.10a: Show that \(L\) is not perpendicular to \(\Pi \).
• 16M.1.hl.TZ2.10b: Given that \(L\) lies in the plane \(\Pi \), find the value of \(p\) and the value of \(q\).
• 16M.1.hl.TZ1.11b: (i)     Show that \(L\) has direction...
• 16N.1.hl.TZ0.8a: find the value of \(a\);
• 17M.2.hl.TZ2.9a: Find the vector equation of the line (BC).
• 17N.1.hl.TZ0.2a: Find a vector equation of the line L passing through the points A and B.
• 18M.1.hl.TZ2.9d: Find the vector equation of the straight line passing through M and normal to the plane \(\Pi...

Simple applications to kinematics.

• 11M.2.hl.TZ1.10: Port A is defined to be the origin of a set of coordinate axes and port B is located at the point...
• 09M.2.hl.TZ1.11: (a)     Find the coordinates of P when \(t = 0\) . (b)     Show that P moves along the line...
• 15N.2.hl.TZ0.10a: find the vectors \({{a}}\) and \({{b}}\).

The angle between two lines.

• 09M.2.hl.TZ1.5: Find the angle between the lines \(\frac{{x - 1}}{2} = 1 - y = 2z\) and \(x = y = 3z\) .
• 15M.2.hl.TZ2.13b: Find the acute angle between the lines \({L_1}\) and \({L_2}\).
• 16N.2.hl.TZ0.2: Find the acute angle between the planes with equations \(x + y + z = 3\) and \(2x - z = 2\).