If a=3hati+hatj-4hatk,b=6hati+5hatj-2hatk, then find the area of a triangle whose adjacent sides are determined by a and b.

If a=3hati+hatj-4hatk,b=6hati+5hatj-2hatk, then find the area of a tri

1.	If a=3hati+hatj-4hatk,b=6hati+5hatj-2hatk, then find the area of a triangle whose adjacent sides are determined by a and b.
Answer» `12.5"SQ unit" ` `11.5"sq unit" ` `135"sq unit" ` `13.5"sq unit" ` Solution :Cross product of VECTOR a and b `axxb=\|UNDERSET(6,5,-2)underset(3,1,-4)hati,HATJ,hatk\|` `=hati(-2+20)-hatj(-6+24)+(15+6)=18hati-18hatj+9hatk` magniutde of a and b `\|axxb\|=sqrt((18)^(2)+(-18)^(2)+(9)^(2))=sqrt(729)=27` `therefore "Areaof" Delta=(1)/(2)\|axxb\|=(27)/(2)=13.5"sq unit" `