Question

Point (1,2), (1-3), 1-4,5
,10,ol, (3, 3)​

Answer 1

Answer:

ANSWER

AB

=(2−4,3−5,4−10)=(−2,−2,−6)

AB

=−2

i

^

−2

j

^

−6

k

^

BC

=(1−2,2−3,−1−4)=(−1,−1,−5)

BC

=−1

i

^

−1

j

^

−5

k

^

Equation of

AB

=4

i

^

+5

j

^

+10

k

^

+μ(−2

i

^

−2

j

^

−6

k

^

)

Equation of

BC

=2

i

^

+3

j

^

+4

k

^

+μ(

i

^

+

j

^

+5

k

^

)

Let the fourth point be (a,b,c)

In a parallelogram diagonals bisect each other

∴ Midpoint of vector AC= midpoint of vector BD

2

4+1

,

2

5+2

,

2

10−1

=

2

2+a

,

2

3+b

,

2

4+c

⇒

2

5

=

2

2+a

⇒x=3

⇒

2

7

=(3+b)⇒b=4

⇒

2

9

=

2

4+c

⇒c=5

(a,b,c)=(3,4,5)