Question

Consider the vectors \( \bar a = i – 7j + 7k; \bar b = 3i – 2j + 2k\)

(a) Find \(\bar {ab}\).

(b) Find the angle between \(\bar a \,and\, \bar b\)

(c) Find the area of parallelogram with adjacent sides \(\bar a \,and\, \bar b\)

Answer 1

(a) \(\bar a. \bar b\) = (i – 7j + 7k).(3i – 2j + 2k)

= 3 + 14 + 14 = 31

(b) 

(c) 

= i(-14 + 14) - j(2 - 21) + k(-2 + 21)

= 19j + 19k

Area of the parallelogram = \(\sqrt{19^2 + 19^2} = 19\sqrt{2}\)