Using this figure answer the following questions. ​ 1. Find overline (OA,OB ,OC) 2. Find overline OD 3. Find the coordinate of the vertex D. ​

Question

Using this figure answer the following questions.

1. Find \(\overline {OA}\), \(\overline {OB}\), \(\overline{OC}\)

2. Find \(\overline{OD}\) 

3. Find the coordinate of the vertex D.

Answer 1

1. \(\overline{OA}\) = (3 – 1)i + (-1 – 2)j + (7 – 3)k = 2i – 3j + 4k

\(\overline {OB}\) = (2 – 1)i + (4 – 2)j +(2 – 3)k = i + 2j – k

\(\overline {OC}\)= (4 – 1)i + (1 – 2 )j + (5 – 3 )k = 3i – j + 2 k.

2. From the figure,

3. Let the vertex of D be (x , y , z),

Then, \(\overline {OD}\) = (x – 1)i + (y – 2)j + (z – 3)k.

But we have,

\(\overline {OD}\)= 6i – 2j + 5k = (x – 1)i + (y – 2)j +(z – 3)k

x – 1 = 6 ⇒ x = 7, y – 2 = -2 ⇒ y = 0, z – 3 = 5 ⇒ z = 8.