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Question

If |a|=26,b=7 and a×b=35, Find a.b

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Solution

We have

a=26

b=7

a×b=35

We know that

A×B=ABsinθ

So,

a×b=absinθ

35=26×7sinθ

sinθ=526

We know that

sinθ=HeightHypotenuse

Therefore,

Height=5

Hypotenuse=26

Base=(Hypotenuse)2(Height)2

Base=261

Base=25=5

Therefore,

cosθ=BaseHypotenuse

cosθ=126

Since,

ab=abcosθ

ab=26×7×126

ab=7

Hence, this is the answer.


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