Question

The volume of a right triangular prism $ABC{A}_1{B}_1{C}_1$ is equal to 3. Than the co-ordinates of the vertex A1, if the co-ordinates of the base vertices of the prism are A(1, 0, 1), B(2, 0, 0) and C(0, 1, 0)

• A. (–2, 2, 2) or (0, –2, 1)
• B. (2, 2, 2) or (0, –2, 0)
• C. (0, 2, 0) or (1, –2, 0)
• D. (3, –2, 0) or (1, –2, 0)

Answer 1

The correct option is B (2, 2, 2) or (0, –2, 0)

Volume = Area of base $\times$ height

$3={\frac{1}{2}}^{\prime }{\sqrt{2}}^{\prime }{\sqrt{3}}^{\prime }hh={\sqrt{6}}^{\prime }(A_{1}A{)}^2=h_2=6\overline{A_{1}A}.\overline{AB}=0\overline{A_{1}A}.\overline{AC}=0\overline{A{A}_1}.\overline{BC}=0$
solving we get position vector of $A_1$ are (0, –2, 0) or (2, 2, 2)