Question

given that (8u-v) perpendicular (4u+3v) and [v]=2[u] find the angle between u and v.

Answer 1

if two vectors are perpendicular, it means their dot product is zero

Answer 2

ok

Answer 3

\[(8u-v)\cdot(4u+3v)=0\\
32u\cdot u-4u\cdot v+24u\cdot v-3v\cdot v=0\\
20u\cdot v =3(2u)^2-32u^2\\
20u\cdot v+20u^2=0\\
20u\cdot (v+u)=0\\
u=0;\text{OR}u+v=0\\
u=-v
\]
angle between them is 180°?

Answer 4

how?

Answer 5

how do u know its 180?

Answer 6

-ve sign

Answer 7

and isn't it supposed to be 20u⋅v+26u2=0? not 20

Answer 8

3*2^2-32=-20

Answer 9

oh ok thanks

Answer 10

so the angle can also be 0 right?

Answer 11

no. if 0, then sign is +ve

Answer 12

but how do u know that -ive sign means 180?