DP Mathematics HL Questionbank

• Syllabus

4.7

Sub sections and their related questions

Intersections of: a line with a plane; two planes; three planes.

• 12M.2.hl.TZ1.4: The planes \(2x + 3y - z = 5\) and \(x - y + 2z = k\) intersect in the line...
• 12M.2.hl.TZ2.11d: The z-axis meets the plane \( \div \) at the point P. Find the coordinates of P.
• 08M.1.hl.TZ1.11: The points A, B, C have position vectors i + j + 2k , i + 2j + 3k , 3i + k respectively and lie...
• 08M.2.hl.TZ1.5: Find the vector equation of the line of intersection of the three planes represented by the...
• 08N.2.hl.TZ0.10: (a)     Write the vector equations of the following lines in parametric...
• 10N.1.hl.TZ0.7: Consider the plane with equation \(4x - 2y - z = 1\) and the line given by the parametric...
• 10N.2.hl.TZ0.12: The diagram shows a cube OABCDEFG.     Let O be the origin, (OA) the x-axis, (OC) the y-axis...
• 11N.2.hl.TZ0.13c: The point P has coordinates (−2, 4, 1) , the point Q lies on \({\Pi _3}\) and PQ is perpendicular...
• 09M.2.hl.TZ1.7: (a)     If \(a = 4\) find the coordinates of the point of intersection of the three...
• 14M.1.hl.TZ1.12f: Find the coordinates of E, the reflection of the point D in the plane \({\mathit{\Pi }}\).
• 14M.1.hl.TZ2.12d: (i)     Find the value of \(k\). (ii)     Find the point of intersection P of the line \({L_3}\)...
• 13N.1.hl.TZ0.11f: Find conditions on \(\alpha \) and \(\beta \) if the plane \({\Pi _3}\) does not intersect with...
• 14M.1.hl.TZ1.12e: Find the coordinates of D, the point of intersection of the line \(L\) with the plane whose...
• 14M.1.hl.TZ2.12c: Find the Cartesian equation of the plane \({\Pi _1}\).
• 13N.1.hl.TZ0.11e: Find the value of \(\alpha \) if all three planes contain \({L_1}\).
• 14N.2.hl.TZ0.5b: The line \({l_3}\) passing through the point \((4,{\text{ }}0,{\text{ }}8)\) is perpendicular to...
• 16M.1.hl.TZ2.1: The following system of equations represents three planes in space. \[x + 3y + z =  -...
• 16M.1.hl.TZ2.10c: (i)     Show that \(p =  - 2\). (ii)     If \(L\) intersects \(\Pi \) at \(z =  - 1\), find the...
• 16M.1.hl.TZ1.11c: Given the vector \(\overrightarrow {{\text{AB}}} \) is perpendicular to \(L\) find the value of...
• 16M.1.hl.TZ1.11d: Show that \({\text{AB}} = 3\sqrt 2 \).
• 16M.1.hl.TZ1.11e: Find the coordinates of the two possible positions of \(P\).
• 16N.1.hl.TZ0.1: Find the coordinates of the point of intersection of the planes defined by the equations...
• 16N.1.hl.TZ0.8b: determine the coordinates of the point of intersection P.
• 17N.1.hl.TZ0.2b: Find the coordinates of the point of intersection of the line L with the plane Π.
• 18M.1.hl.TZ1.10d: Show that P is the midpoint of AD.
• 18M.1.hl.TZ1.10e: Find the area of the triangle OPQ.
• 18M.1.hl.TZ2.9f.i: Find the coordinates of X, Y and Z.
• 18M.1.hl.TZ2.9f.ii: Find YZ.

Angle between: a line and a plane; two planes.

• 12M.2.hl.TZ1.4: The planes \(2x + 3y - z = 5\) and \(x - y + 2z = k\) intersect in the line...
• 12M.2.hl.TZ2.11e: Find the angle between the line \(\frac{{x - 2}}{3} = \frac{{y + 5}}{4} = \frac{z}{2}\) and the...
• 12N.2.hl.TZ0.13a: Find the angle between the planes \({\pi _1}\)and \({\pi _2}\) .
• 08M.1.hl.TZ1.11: The points A, B, C have position vectors i + j + 2k , i + 2j + 3k , 3i + k respectively and lie...
• 08M.2.hl.TZ1.3: A ray of light coming from the point (−1, 3, 2) is travelling in the direction of vector...
• 11M.2.hl.TZ2.11g: A second plane, \({\prod _2}\) , has equation x − 2y + z = 3. Calculate the angle between the two...
• 10M.2.hl.TZ1.11: A plane \(\pi \) has vector equation r = (−2i + 3j − 2k) + \(\lambda \)(2i + 3j + 2k) + \(\mu...
• 14N.2.hl.TZ0.1: Consider the two planes      \({\pi _1}:4x + 2y - z = 8\)      \({\pi _2}:x + 3y + 3z =...
• 18M.1.hl.TZ1.10b: Find the angle between the faces ABD and BCD.