Question

if A =2i+3j+k and B=i+j .Find |A+B| and |A-B|of​

Answer 1

We are given two vectors,

• A = 2i + 3j + k
• B = i + j

We are requested to find the magnitude of resultant vectors of A + B and A - B

For finding the resultant vector of sum of two vectors in component form, following rule can be used,

Given two vectors,

• A = Aₓi + Aᵧj + A₂k
• B = Bₓi + Bᵧj + B₂k

Addition and subtraction of vectors can be found,

Addition :-

• R = (Aₓ + Bₓ)i + (Aᵧ + Bᵧ)j + (A₂ + B₂)k

Subtraction :-

• R = (Aₓ - Bₓ)i + (Aᵧ -Bᵧ)j + (A₂ - B₂)k

So, Let's find A + B

⇒ R(A + B) = (2 + 1)i + (3 + 1)j + (1 + 0)k

⇒ R(A + B) = 3i + 4j + k

But, we have to find the magnitude, so

⇒ | A + B | = √{ (3)² + (4)² + (1)² }

⇒ | A + B | = √{ 9 + 16 + 1 }

⇒ | A + B | = √26

Similarly, Let's find A - B

⇒ R(A - B) = (2 - 1)i + (3 - 1)j + (1 - 0)k

⇒ R(A - B) = i + 2j + k

But, we are requested to find the Magnitude, so

⇒ | A - B | = √{ (1)² + (2)² + (1)² }

⇒ | A - B | = √( 1 + 4 + 1 )

⇒ | A - B | = √6

Hence,

• | A + B | = √26
• | A - B | = √6