2025 RI Promo Q6
2025 RI Promo Q6
Junior College 1
7 marks
- The non-zero vectors \(\mathbf{a}\), \(\mathbf{b}\), and \(\mathbf{c}\) are such that \(3\mathbf{a}\times\mathbf{b}=2\mathbf{b}\times\mathbf{c}\), where \(3\mathbf{a}\ne -2\mathbf{c}\). Find a linear relationship between \(\mathbf{a}\), \(\mathbf{b}\), and \(\mathbf{c}\).[3]
The variable position vector \(\mathbf{v}\) satisfies the equation
\(\mathbf{v}\times(-\mathbf{i}+2\mathbf{j}+\mathbf{k})=a\mathbf{i}+\mathbf{j}+\mathbf{k},\)
where \(a\) is a non-zero constant.
- Show that \(a=3\).[1]
- Hence, by finding the set of position vectors \(\mathbf{v}\), describe geometrically the set of points represented by the position vectors \(\mathbf{v}\).[3]
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Answer:(a) \(\mathbf b=k(3\mathbf a+2\mathbf c)\), \(k\ne0\) (b)(i) \(a=3\) (b)(ii) line \(\mathbf v=(-1,3,0)+\lambda(-1,2,1)\)
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