Question

if a vector + b vector is equal to c vector and a square + b square is equal to c square then find angle the between them

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Answer 1

Formula used:

a→b→=abcosθ

Where the angle between two vectors a→ and b→ is θ .

Complete step by step answer:

The resultant vector of the two vectors a→ and b→ is c→ i.e a→+b→=c→………(1)

The modulus of the two vectors a→ and b→is a and b .

The sum of a and bis c i.e a+b=c…………(2)

By squaring both sides of eq. (1) we get,

(a→+b→)2=c2

⇒c2=(a→+b→)(a→+b→)

⇒c2=a2+b2+2a→.b→

Since a→.b→=abcosθ

⇒c2=a2+b2+2abcosθ

⇒c2=a2+b2+2abcosθ

⇒(a+b)2=a2+b2+2abcosθ fromtheeq.$(2)$

⇒a2+b2+2ab=a2+b2+2abcosθ

⇒cosθ=1

⇒θ=0∘

So, the angle between the vectors a→ and b→ is θ=0∘.