Question

plz solve and explain it​

Answer 1

first take out the angle between these two Vectors

we know,thatA.B=|A||B|cos∅cos∅=A.B/|A||B|......i)

this is the dot product rule

Now,

Let,A=3i+4j and B=i+j

A.B=3×1+4×1=7

also,

|A|=(3^2+4^2)^1/2=5

|B|=(1^2+1^2)^1)2=√2

putting these value in first we get

cos∅=7/5√2

cos^2∅=49/50

1-sin^2∅=49/50

sin^2∅=1/50

sin∅=1/5√2

vector perpendicular to i+j will be (3i+4j)sin∅

magnitude of that vector=(9+16)^1/2×1/√2×5=1/√2.......ii)

let,the vector perpendicular to i+j,be ai+bj

their dot product will be 0

(i+j)(ai+bj)=0

a+b=0

a=-b

this (-) signshows unit vecotor perpendicular to i+j

will be (-i+j)/√2

multiplying this unit perpendicular vector by 1/√2,

required,vector=1/√2×(-i+j)×1/√2=1/2(-i+j)

{hope it helps you}