​ 1. Evaluate overline (AB.AC) 2. Find overline AD​ 3. Find the coordinates of D.

Question

Using the figure answer the following questions

1. Evaluate \(\overline{AB}.\overline{AC}\)

2. Find \(\overline {AD}\).

3. Find the coordinates of D.

Answer 1

1. \(\overline{AB}\) = p.v of B – p.v of A= -4i + 0j + 3k

\(\overline{AC}\) = p.v of C – p.v of A = 0i – 4 j + 4k

\(\overline {AB}.\overline{AC}\) = -4 × 0 + 0 × -4 + 3 × 4 = 12

2. 

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

⇒ \(\overline{AD}\) = (x – 3)i + (y – 2)j + (z – 1)k,