Question

Show that vectors a=2i+3j+6k
b=3i-6j+2k and c=6i+2j-3k are
mutually perpendicular.​

Answer 1

Dear Student,

◆ Proof -

Given vectors are -

a = 2i+3j+6k

b = 3i-6j+2k

c = 6i+2j-3k

We know that dot product of perpendicular vectors is zero.

For a and b,

a.b = (2i+3j+6k).(3i-6j+2k)

a.b = 2×3 - 3×6 + 6×2

a.b = 6 - 18 + 12

a.b = 0

Thus, a and b are perpendicular.

For b and c,

b.c = (3i-6j+2k).(6i+2j-3k)

b.c = 3×6 - 6×2 - 3×2

b.c = 18 - 12 - 6

b.c = 0

Thus, b and c are perpendicular.

For a and c,

a.c = (6i+2j-3k).(2i+3j+6k)

a.c = 6×2 + 2×3 - 3×6

a.c = 12 + 6 - 18

a.c = 0

Thus, a and c are perpendicular.

Hope that helps...

Answer 2

Explanation:

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