Consider the parallelogram ABCD 1. ​ Find overline (AB and AD). 2. Find the area of the parallelogram ABCD.

Question

Consider the Parallelogram ABCD

1. Find \(\overline {AB}\) and \(\overline{AD}\) 
2. Find the area of the parallelogram ABCD. 
3. Find \(\overline {AC}\). 
4. Find co-ordinate of C. 

Answer 1

1. \(\overline {AB}\) = p.v of B – p. v of A

= 3i + 5j + 8k – (i + 2j + k) = 2i + 3j + 7k

\(\overline{AD}\) = p.v of D – p. v of A

= i + 3j + 2k – (i + 2j + k)= 0i + j + k.

2. 

3. By triangle inequality;

4. Let the co-ordinate of C be (x, y, z)

Then, \(\overline{AC}\)= (x – 1)i + (y – 2)j + (z – 1)k = 2i + 4j + 8k

x – 1 = 2 ⇒ x = 3, y – 2 = 4 ⇒ y = 6,

z – 1 = 8 ⇒ z = 9

Co-ordinate of C is (3, 6, 9).