Question

༒ Bʀᴀɪɴʟʏ Sᴛᴀʀs

༒Mᴏᴅᴇʀᴀᴛᴇʀs

༒Other best user

if a = 5i - j -3k and b= i+3j-5k, then show that the vectors a+b and a-b are perpendicular

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Answer 1

$\tt\huge\purple{hello!!!}$

HERE IS UR ANSWER

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Given

a = 5i - j -3k and

b= i+3j-5k

To prove

The condition of two vectors are to be perpendicular to each other if dot product of two vectors is zero.

i.e, A.B=0

Proof

A=a+b=6i+2j-8k

B=a-b=4i-4j+2k

LHS

A.B=(6i+2j-8k).(4i-4j+2k)

◇In scalar product ◇

$\fbox{(i.i=1,j.j=1,k.k=1}$

$\fbox{Also,i.j=0,j.k=0,k.i=0}$

= 24-8-16

= 0

RHS

=0

$\bold\pink{hence\:proved!!}$

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