The area of the triangle, whose vertices are at the points (2$$, $$1$$, $$1), (3$$, $$1$$,$$2) and $$(-$$ $$4$$,$$0$$, $$1)$$ is

Question

Infinity Learn · Accepted Answer

∵Δ$$yz=12y1z11y2z21y3z31$$,Δ$$zx=12z1x11z2x21z3x31$$,Δ$$xy=12x1y11x2y21x3y31$$∴ Δ$$yz=121$$    $$1$$    $$11$$    $$2$$    $$10$$    $$1$$    $$1=12$$|[$$1(2$$−$$1)$$−$$1(1$$−$$0)+1(1$$−$$0)$$]|$$=12$$|[$$1$$−$$1+1$$]|$$=12$$Δ$$zx=121212311$$−$$41=12$$|[$$1(3+4)$$−$$2(2$$−$$1)+1($$−$$8$$−$$3)$$]|$$=12$$|[$$7$$−$$2$$−$$11$$]|$$=3$$Δ$$xy=12211311$$−$$401=12$$|[$$2(1$$−$$0)$$−$$1(3+4)+1(0+4)$$]|$$=12Area$$ of triangle,Δ$$=$$Δ$$yz2+$$Δ$$zx2+$$Δ$$xy2=122+(3)2+122=14+9+14=382$$ sq unit

The area of the triangle, whose vertices are at the points (2, 1, 1), (3, 1,2) and (- 4,0, 1) is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material