Class 12 Vector Algebra · Case Study4 Markscross_product_applications
Class 12 Maths · Vector Algebra · Case Study #124
A tetrahedral plant holder has vertices A=(1,2,3), B=(3,2,1), C=(2,1,2), D=(3,4,3). Coordinates use a common length unit. Answer (i), (ii), and either (iii)(a) or (iii)(b).
Part (1) 1 Marks
Find AB.
Answer: AB=(2,0,−2).
- Use AB=B−A.
- AB=(3−1,2−2,1−3)=(2,0,−2).
Part (2) 1 Marks
Find CD.
Answer: CD=(1,3,1).
- Use CD=D−C.
- CD=(3−2,4−1,3−2)=(1,3,1).
Part (3) 2 Marks
Find the unit vector along BC.
Answer: (−1,−1,1)/√3.
- Compute BC=C−B=(−1,−1,1).
- Its norm is √(1+1+1)=√3.
- The unit vector along BC is (−1,−1,1)/√3.
Part (4) 2 Marks
Find the area of triangle BCD.
Answer: √6 square units.
- Use BC=(−1,−1,1) and BD=D−B=(0,2,2).
- BC×BD=(−4,2,−2), with norm √24=2√6.
- Triangle area is half this norm: √6 square units.