Moderate -0.5 This is a straightforward application of the scalar triple product formula for tetrahedron volume: V = (1/6)|a·(b×c)|. While it requires knowledge of vectors and the cross product (Further Maths content), the calculation is routine with no problem-solving insight needed. The 3-mark allocation confirms it's a standard procedural question, making it slightly easier than average overall.
Determine the volume of tetrahedron \(OABC\), where \(O\) is the origin and \(A\), \(B\) and \(C\) are, respectively, the points \((2, 3, -2)\), \((2, 0, 4)\) and \((6, 1, 7)\). [3]
Question 1:
1 | use of formula V = 1 a (cid:127) b×c or equivalent NB b × c = –4i + 10j + 2k
6
2 3 −2
attempt at relevant scalar triple product = 2 0 4 = 18
6 1 7
(or a scalar and a vector product)
V = 3 cso | M1
M1
A1
[3]
Determine the volume of tetrahedron $OABC$, where $O$ is the origin and $A$, $B$ and $C$ are, respectively, the points $(2, 3, -2)$, $(2, 0, 4)$ and $(6, 1, 7)$. [3]
\hfill \mbox{\textit{Pre-U Pre-U 9795/1 2015 Q1 [3]}}