Question

if two sides of a triangle be formed by vectors p & q show that the area of a triangle is 1/2 × | vector p × vector q |.​

Answer 1

Explanation:

Since

a

.

b

=0, the angle between the vectors

a

and

b

is

2

π

Now, adding these two vectors, we get

c

=

a

+

b

=7

i

^

+5

j

^

+

k

^

So, the other two angles of the triangle are given by

α=cos

−1

∣

∣

∣

∣

c

∣

∣

∣

∣

∣

∣

∣

∣

a

∣

∣

∣

∣

c

.

a

=cos

−1

7

2

+5

2

+1

2

3

2

+6

2

+(−2)

2

(7)(3)+(5)(6)+(1)(−2)

=cos

−1

75

7

β=cos

−1

∣

∣

∣

∣

c

∣

∣

∣

∣

∣

∣

∣

∣

b

∣

∣

∣

∣

c

.

b

=cos

−1

7

2

+5

2

+1

2

4

2

+(−1)

2

+3

2

(7)(4)+(5)(−1)+(1)(3)

=cos

−1

75

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