Which pairs (if any) of these vectors are are perpendicular,parallel, Have an angles less than π/2 between them, Have an angle of more than π/2 between them?

Question

Consider the vectors

a =4i +j −k

b =i +j +5k

c =i +4j −k

d =−4i −j +k

g =i −4j .

Which pairs (if any) of these vectors are

(a) Are perpendicular?

(b) Are parallel?

(c) Have an angles less than π/2 between them?

(d) Have an angle of more than π/2 between them?

(Enter none or a pair or list of pairs, e.g., if a⃗ is at an angle greater than pi/2 from b⃗ and c⃗ , enter (a,b),(a,c).)

Answer 1

Hello,

a =4i +j −k

b =i +j +5k

c =i +4j −k

d =−4i −j +k

g =i −4j .

for finding which vectors are perpendicular it is enough you find dot product any two given vector.

a.b = 4 +1 -5 = 0 a perpendicular b

a.c = 4+4 +1 ≠ 0

a.d = -16-1-1 ≠0

a.g = 4-4+0 = 0 a perpendicular g

you need to try for all pairs of given vectors

for finding angle between two vectors, use this formula: cos ø = ( a.b ) / ||a||.||b||

as an example:

a&d -------> cos ø = -18/√18.√18 = -1 ---- ø = 180 they are parallels

a & c-------> cos ø = 9/√18.√18 = 1/2 ø = 60

by doing that you will know the situation between all given victors.

I hope it is useful,

Minoo

you need to do for any pair of given vectors