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...