Question

11. If a, b, c are three vectors such that a × b = c and
b × c = a, show that a, b, c are orthogonal in
pairs and |b| = 1, Icl = |a| ​

Answer 1

Answer:

∵a⊥(b+c)

∴a.(b+c)=0⇒a.b+a.c=0 ...(1)

Similarly b⊥(c+a)⇒b.c+b.a=0 ...(2)

and c⊥(a+b)=0⇒c.a+c.b=0 ...(3)

Adding (1),(2),(3), we get

2(a.b+b.c+c.a)=0

Now, (a+b+c)

2

=a

2

+b

2

+c

2

+2(a.b+b.c+c.a)

=∣a∣

2

+∣b∣

2

+∣c∣

2

+0=3

2

+4

2

+c

2

=50

Hence ∣a+b+c∣=5

2