2.

i. Find the magnitude of vector a = i + 2j + 2k.

ii. For b = 2i − j + 2k and c = 2i + 2j − k, show that b − c is perpendicular to a.

iii. Find the volume of the parallelepiped, with three concurrent edges formed by the

position vectors a, b and c.

i.The magnitude of a is 3.(simple)

ii.b-c=-3j+3k and (b-c).a=0 and hence perpendicular.

iii.V=[a b c]=det 1 2 2  =21 cubic units.

                          2-1 2

                          2 2-1

mag is: [(1)² +(2)² +(2)²]^1/2 = 3







since (b-c).a (dot product) = 0  => (b-c) & a  r perpendicular 2 each other







well u mite not have learnt this formula now but its in class 12th -



vol of a parallelopiped formed by 3 vectors = |a.(b*c)|



where a,b,c = vectors



* = cross product