Standard +0.8 This is a Further Maths question requiring knowledge of the scalar triple product formula for tetrahedron volume (V = 1/6|a·(b×c)|). While the calculation itself is mechanical once the formula is known, it's a specialized topic beyond standard A-level, involves vector cross product and determinant evaluation, making it moderately harder than average but still a direct application question.
2 Find the volume of tetrahedron OABC , where O is the origin, \(\mathrm { A } = ( 2,3,1 ) , \mathrm { B } = ( - 4,2,5 )\) and \(\mathrm { C } = ( 1,4,4 )\).
Question 2:
2 | V = 1a(cid:152)b(cid:117)c
6
(cid:167)2(cid:183) (cid:167)(cid:16)12(cid:183)
(cid:168) (cid:184) (cid:168) (cid:184)
= 1(cid:117) 3 (cid:152) 21 = 3.5
6 (cid:168) (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:169)1(cid:185) (cid:169)(cid:16)18(cid:185) | M1
A1
A1 FT
[3] | 1.1a
1.1
1.1 | n
e
Attempt to use the triple scalar
product
m
A correct vector product BC
BC FT their vector product if seen
2 Find the volume of tetrahedron OABC , where O is the origin, $\mathrm { A } = ( 2,3,1 ) , \mathrm { B } = ( - 4,2,5 )$ and $\mathrm { C } = ( 1,4,4 )$.
\hfill \mbox{\textit{OCR Further Additional Pure Q2 [3]}}