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Question

The angle between the vectors ¯u=<3,0> and ¯v=<5,5> is ___


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Solution

We know that for two vectors a and b their dot product

a.b=|a||b|cos θSo cos θ=a.b|a||b|

Now here

Cos θ=u.v|v||u| ...(1)

|v|=32+02=3|v|=52+52=50Also u.v=<3,0>.<5,5>

=(3×5)+(0×5) [(a1^i+a2^j).(b1^i+b2^j)=(a1b2+a2b2)]

So substituting the values in (1)

We get

Cos θ=153×50=153×5×2=12Cos θ12 θ=45, which is the correct answer.


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