Question
Find the area of the triangle whose vertices are (1, 2, 4), (-2, 1, 2), (2, 4, -3).
Solution
Let A (1, 2, 4), B (– 2, 1, 2), C (2, 4, – 3) be vertices of Δ ABC.
Direction-ratios of AB are – 2, – 1, 1 – 2, 2 – 4 i.e., – 3, – 1,– 2 respectively.
Direction-ratios of AC are 2 – 1, 4 – 2, – 3 – 4 i.e., 1, 2, – 7 respectively.
Direction-ratios of AB are – 2, – 1, 1 – 2, 2 – 4 i.e., – 3, – 1,– 2 respectively.
Direction-ratios of AC are 2 – 1, 4 – 2, – 3 – 4 i.e., 1, 2, – 7 respectively.
Tips: -
Note on parallelopiped and cube
(i) A parallelopipcd is a solid bounded by three pairs of parallel plane faces.
(ii) A rectangular parallelopiped is parallelopiped whose faces are all rectangles.
(iii) A cube is a parallelopiped whose faces are all squares.
