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4.6

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Topic 4 - Core: Vectors » 4.6

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Directly related questions

18M.1.hl.TZ2.9e: Find the Cartesian equation of \(\Pi \).
18M.1.hl.TZ1.10c: Find the Cartesian equation of \({\Pi _3}\).
18M.1.hl.TZ1.10a: Find the Cartesian equation of the plane \({\Pi _1}\), passing through the points A , B and D.
16N.1.hl.TZ0.4b: Hence find the Cartesian equation of the plane containing the vectors a and b, and passing...
17M.2.hl.TZ2.9f: Find a vector perpendicular to the plane Π\(_3\).
17M.2.hl.TZ2.9e: Verify that 2j + k is perpendicular to the plane Π\(_2\).
17M.2.hl.TZ2.9d: Show that the line (BC) lies in the plane Π\(_1\).
17M.2.hl.TZ2.9c: Find the Cartesian equation of the plane Π\(_1\), which passes through C and is perpendicular to...
17M.2.hl.TZ1.7: Find the Cartesian equation of plane Π containing the points...
12M.2.hl.TZ1.4: The planes \(2x + 3y - z = 5\) and \(x - y + 2z = k\) intersect in the line...
12M.2.hl.TZ1.13b: Find the Cartesian equation of \(\Pi \), the plane passing through A, B, and C.
12M.2.hl.TZ1.13c(i)(ii): (i) Find the Cartesian equation of \({\Pi _1}\) , the plane perpendicular to (AB)...
12M.2.hl.TZ2.11c: The plane \( \div \) is parallel to both the line in part (b) and the line...
12N.2.hl.TZ0.13d: Determine a Cartesian equation of the plane \({\pi _3}\) containing both lines \({L_1}\) and...
08M.1.hl.TZ2.11: Consider the points A(1, −1, 4), B (2, − 2, 5) and O(0, 0, 0). (a) Calculate the cosine of...
11M.2.hl.TZ2.11d: Find the Cartesian equation of the plane, \({\prod _1}\) , containing the parallelogram PQRS.
SPNone.2.hl.TZ0.10a: (i) Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \) . (ii) ...
10M.1.hl.TZ1.3: (a) Show that the two planes \[{\pi _1}:x + 2y - z = 1\] \[{\pi _2}:x + z = - 2\] are...
10M.1.hl.TZ2.12a: Consider the vectors a = 6i + 3j + 2k, b = −3j + 4k. (i) Find the cosine of the angle...
10M.2.hl.TZ1.11: A plane \(\pi \) has vector equation r = (−2i + 3j − 2k) + \(\lambda \)(2i + 3j + 2k) + \(\mu...
13M.1.hl.TZ2.11c: Find the Cartesian equation of the plane containing the triangle ABC.
11N.2.hl.TZ0.13b: Show that the plane \({\Pi _3}\) which is perpendicular to \({\Pi _1}\) and contains L, has...
11M.1.hl.TZ1.11b: Find the Cartesian equation of the plane \(\prod \) that contains the face ABC.
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.TZ1.12c: Show that an equation of the plane \({\mathit{\Pi }}\), containing the square OABC, is...
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.TZ0.11c: Show that the Cartesian equation of the plane \({\Pi _1}\), containing the triangle ABC, is...
14M.1.hl.TZ2.12c: Find the Cartesian equation of the plane \({\Pi _1}\).
14N.2.hl.TZ0.5a: Find the Cartesian equation of \(\pi \).

Sub sections and their related questions

Vector equation of a plane \(r = a + \lambda b + \mu c\) .

10M.2.hl.TZ1.11: A plane \(\pi \) has vector equation r = (−2i + 3j − 2k) + \(\lambda \)(2i + 3j + 2k) + \(\mu...
11N.2.hl.TZ0.13b: Show that the plane \({\Pi _3}\) which is perpendicular to \({\Pi _1}\) and contains L, has...
18M.1.hl.TZ2.9e: Find the Cartesian equation of \(\Pi \).

Use of normal vector to obtain the form \(r \cdot n = a \cdot n\) .

11M.2.hl.TZ2.11d: Find the Cartesian equation of the plane, \({\prod _1}\) , containing the parallelogram PQRS.
SPNone.2.hl.TZ0.10a: (i) Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \) . (ii) ...
11M.1.hl.TZ1.11b: Find the Cartesian equation of the plane \(\prod \) that contains the face ABC.
13N.1.hl.TZ0.11c: Show that the Cartesian equation of the plane \({\Pi _1}\), containing the triangle ABC, is...
18M.1.hl.TZ2.9e: Find the Cartesian equation of \(\Pi \).

Cartesian equation of a plane \(ax + by + cz = d\) .

12M.2.hl.TZ1.4: The planes \(2x + 3y - z = 5\) and \(x - y + 2z = k\) intersect in the line...
12M.2.hl.TZ1.13b: Find the Cartesian equation of \(\Pi \), the plane passing through A, B, and C.
12M.2.hl.TZ1.13c(i)(ii): (i) Find the Cartesian equation of \({\Pi _1}\) , the plane perpendicular to (AB)...
12M.2.hl.TZ2.11c: The plane \( \div \) is parallel to both the line in part (b) and the line...
12N.2.hl.TZ0.13d: Determine a Cartesian equation of the plane \({\pi _3}\) containing both lines \({L_1}\) and...
08M.1.hl.TZ2.11: Consider the points A(1, −1, 4), B (2, − 2, 5) and O(0, 0, 0). (a) Calculate the cosine of...
10M.1.hl.TZ1.3: (a) Show that the two planes \[{\pi _1}:x + 2y - z = 1\] \[{\pi _2}:x + z = - 2\] are...
10M.2.hl.TZ1.11: A plane \(\pi \) has vector equation r = (−2i + 3j − 2k) + \(\lambda \)(2i + 3j + 2k) + \(\mu...
10M.1.hl.TZ2.12a: Consider the vectors a = 6i + 3j + 2k, b = −3j + 4k. (i) Find the cosine of the angle...
13M.1.hl.TZ2.11c: Find the Cartesian equation of the plane containing the triangle ABC.
11M.1.hl.TZ1.11b: Find the Cartesian equation of the plane \(\prod \) that contains the face ABC.
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.TZ1.12c: Show that an equation of the plane \({\mathit{\Pi }}\), containing the square OABC, is...
14M.1.hl.TZ2.12d: (i) Find the value of \(k\). (ii) Find the point of intersection P of the line \({L_3}\)...
14M.1.hl.TZ2.12c: Find the Cartesian equation of the plane \({\Pi _1}\).
14N.2.hl.TZ0.5a: Find the Cartesian equation of \(\pi \).
16N.1.hl.TZ0.4b: Hence find the Cartesian equation of the plane containing the vectors a and b, and passing...
18M.1.hl.TZ2.9e: Find the Cartesian equation of \(\Pi \).