DP Mathematics SL Questionbank

• Syllabus

4.3

Sub sections and their related questions

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

• 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 \(\overrightarrow {{\rm{OB}}} \) . (ii)    Find \(\overrightarrow {{\rm{OF}}} \)...
• 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.TZ0.2a(i) and (ii): (i)     Find the velocity vector, \(\overrightarrow {{\rm{AB}}} \) . (ii)    Find the speed of...
• 08N.1.sl.TZ0.2b: Write down an equation of the line L .
• 08M.2.sl.TZ1.9b: The line \({L_1}\) has...
• 08M.2.sl.TZ1.9c(i) and (ii): The line \({L_2}\) passes through A and is parallel to \(\overrightarrow {{\rm{OB}}} \) . (i)  ...
• 08M.2.sl.TZ1.9d: The line \({L_3}\) 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 \(\overrightarrow {{\rm{PQ}}} \) and \({L_2}\) .
• 12M.1.sl.TZ1.8c: The lines \({L_1}\) and \({L_2}\) 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 \({\boldsymbol{r}} = {\boldsymbol{u}} + s{\boldsymbol{v}}\) . (i)    ...
• 10N.1.sl.TZ0.8c: The lines (AC) and (BD) intersect at the point \({\text{P}}(3{\text{, }}k)\) . Show that...
• 10N.1.sl.TZ0.8d: The lines (AC) and (BD) intersect at the point \({\text{P}}(3{\text{, }}k)\) . Hence find the...
• 10M.1.sl.TZ1.10a: Write down a vector equation for \({L_2}\) in the form...
• 10M.1.sl.TZ1.10b: A third line \({L_3}\) is perpendicular to \({L_1}\) and is represented by...
• 10M.1.sl.TZ1.10c: The lines \({L_1}\) and \({L_3}\) intersect at the point A. Find the coordinates of A.
• 10M.1.sl.TZ1.10d(i) and (ii): The lines \({L_2}\)and \({L_3}\)intersect at point C where...
• 09N.2.sl.TZ0.10b: The line \({L_1}\) may be represented by...
• 09N.2.sl.TZ0.10c: The point \({\text{T}}( - 1{\text{, }}5{\text{, }}p)\) lies on \({L_1}\) . Find the value of...
• 09N.2.sl.TZ0.10d: The point T also lies on \({L_2}\) with equation...
• 09M.1.sl.TZ2.10a: Write down the equation of \({L_1}\) in the form...
• 09M.1.sl.TZ2.10b: The line \({L_2}\) 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.TZ0.4a: Write down the line that is parallel to \({L_4}\) .
• SPNone.2.sl.TZ0.4b: Write down the position vector of the point of intersection of \({L_1}\) and \({L_2}\) .
• SPNone.2.sl.TZ0.4c: Given that \({L_1}\) is perpendicular to \({L_3}\) , find the value of a .
• 11N.1.sl.TZ0.8a(i) and (ii): (i)     Find \(\overrightarrow {{\rm{PQ}}} \) . (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 \({L_2}\) passes through...
• 11N.1.sl.TZ0.8c: The lines \({L_1}\) and \({L_2}\) 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)     \(\overrightarrow {{\rm{OP}}} \) ; (ii)    \(|\overrightarrow {{\rm{OP}}} |\) .
• 11M.2.sl.TZ2.8a: Find \(\overrightarrow {{\rm{AB}}} \) .
• 11M.2.sl.TZ2.8b: Find an equation for \({L_1}\) in the form...
• 11M.2.sl.TZ2.8c: Find the angle between \({L_1}\) and \({L_2}\) .
• 11M.2.sl.TZ2.8d: The lines \({L_1}\) and \({L_2}\) intersect at point C. Find the coordinates of C.
• 13M.1.sl.TZ1.8b: Given that \({L_1}\) is perpendicular to \({L_2}\) , show that \(p = - 6\) .
• 13M.1.sl.TZ1.8a.ii: Hence, write down a vector equation for \({L_1}\) .
• 14M.1.sl.TZ1.8b(i): Hence, write down a direction vector for \({L_1}\);
• 14M.1.sl.TZ1.8b(ii): Hence, write down a vector equation for \({L_1}\).
• 14M.1.sl.TZ1.8d(i): Write down a direction vector for \({L_2}\).
• 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.
• 14N.1.sl.TZ0.10a: Write down the equation of \({L_1}\).
• 14N.1.sl.TZ0.10b: A line \({L_a}\) crosses the \(y\)-axis at a point \(P\). Show that \(P\) has coordinates...
• 15M.1.sl.TZ1.8c: The following diagram shows the line \(L\) and the origin \(O\). The point \(C\) also lies on...
• 16M.2.sl.TZ2.10a: Find \(\overrightarrow {{\text{AB}}} \).
• 16M.2.sl.TZ2.10b: Find the coordinates of C.
• 16M.2.sl.TZ2.10c: Write down a vector equation for \(L\).
• 16M.2.sl.TZ2.10d: Given that...
• 16M.2.sl.TZ2.10e: The point D lies on \(L\) such that...
• 16N.1.sl.TZ0.4a: Find a vector equation of the line that passes through P and Q.
• 17M.1.sl.TZ1.8a.ii: Hence, write down a vector equation for \({L_1}\).
• 17M.1.sl.TZ1.8b: A second line \({L_2}\), has equation r =...
• 17M.1.sl.TZ1.8c: The lines \({L_1}\) and \({L_1}\) intersect at \(C(9,{\text{ }}13,{\text{ }}z)\). Find \(z\).
• 17M.1.sl.TZ1.8d.i: Find a unit vector in the direction of \({L_2}\).
• 17M.1.sl.TZ1.8d.ii: Hence or otherwise, find one point on \({L_2}\) which is \(\sqrt 5 \) units from C.
• 17N.1.sl.TZ0.9a.i: Show that...
• 17N.1.sl.TZ0.9a.ii: Find a vector equation for \(L\).
• 17N.1.sl.TZ0.9b: Find the value of \(p\).
• 17N.1.sl.TZ0.9c: The point D has coordinates \(({q^2},{\text{ }}0,{\text{ }}q)\). Given that...
• 18M.1.sl.TZ1.9a: Show...
• 18M.1.sl.TZ1.9b.i: Find a vector equation for L.
• 18M.1.sl.TZ1.9b.ii: Point C (k , 12 , −k) is on L. Show that k = 14.
• 18M.1.sl.TZ1.9c.i: Find \(\mathop {{\text{OB}}}\limits^ \to  \, \bullet \mathop {{\text{AB}}}\limits^ \to  \).
• 18M.1.sl.TZ1.9c.ii: Write down the value of angle OBA.
• 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.TZ2.1a: Find a vector equation for L1.
• 18M.1.sl.TZ2.1b: The vector \(\left( \begin{gathered} 2 \hfill \\ p \hfill \\ 0 \hfill \\ \end{gathered} \right)\)...

The angle between two lines.

• 12M.2.sl.TZ2.8a(i), (ii) and (iii): (i)     Find \(\overrightarrow {{\rm{OB}}} \) . (ii)    Find \(\overrightarrow {{\rm{OF}}} \)...
• 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.
• 12M.1.sl.TZ1.8a(i) and (ii): (i)     Show that...
• 12M.1.sl.TZ1.8b: Find the cosine of the angle between \(\overrightarrow {{\rm{PQ}}} \) and \({L_2}\) .
• 12M.1.sl.TZ1.8c: The lines \({L_1}\) and \({L_2}\) intersect at the point R. Find the coordinates of R.
• 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...
• 11M.2.sl.TZ2.8a: Find \(\overrightarrow {{\rm{AB}}} \) .
• 11M.2.sl.TZ2.8b: Find an equation for \({L_1}\) in the form...
• 11M.2.sl.TZ2.8c: Find the angle between \({L_1}\) and \({L_2}\) .
• 11M.2.sl.TZ2.8d: The lines \({L_1}\) and \({L_2}\) intersect at point C. Find the coordinates of C.
• 14M.1.sl.TZ1.8d(ii): Hence, find the angle between \({L_1}\) and \({L_2}\).
• 16M.2.sl.TZ1.10a: Find \(\overrightarrow {{\text{AB}}} \).
• 16M.2.sl.TZ1.10b: Show that...
• 16M.2.sl.TZ1.10c: Find \(\theta \).
• 16M.2.sl.TZ1.10d: (i)     Show that...