Question

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Answer 1

Answer:

We will use Herons formula to find area  formed by the vectors

So,

A=√(s(s-a)(s-b)(s-c))

where s is semiperimeter

s=(a+b+c)/2

Let x,y,z be the described vectors instead of a,b,c

Now,

a=║x-y║

a=║i-j-3k - ( 4i-3j+k)║

a=║-3i + 2j - 4k║

a= √29

a=5.385

b=║y-z║

b=║4i-3j+k - (3i-j + 2k)║

b=║i -2j -k║

b=√6

b=2.449

c=║z-x║

c=║3i-j + 2k - (i-j-3k )║

c=║2i+5k║

c=√29

c=5.385

So,

s=(5.385+5.385+2.449)/2

s=6.6095

Now,

Area will be

A=√(s(s-a)(s-b)(s-c))

A=√6.6095(6.6095-5.385)(6.6095-2.449)(6.6095-5.385)

A=6.4120

So, the area is 6.4120 square units.