Question

Calculate the area of a triangle whose adjacent sides are given by the vectors

A=2i-5j+8k and B=i+3j-4k.

​

Answer 1

ANSWER

Area =

2

1

×∣A×B∣

A×B =15k−20j

∣A×B∣ =25

⟹ Area = 12.5

Answer 2

Explanation:

Let

a

and

b

are adjacent side of a parallelogram, where

a

=2

i

^

+4

j

^

−5

k

^

and

b

=

i

^

+2

j

^

+3

k

^

Let diagonal be

c

Hence

c

=

a

+

b

=2

i

^

+4

j

^

−5

k

^

+

i

^

+2

j

^

+3

k

^

=3

i

^

+6

j

^

−2

k

^

magnitude of

c

=

3

2

+6

2

+2

2

=

9+36+4

=7

Unit vector in direction of

c

=

∣

c

∣

c

=

7

1

(3

i

^

+6

j

^

−2

k

^

)