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 $2x - z = 2$.