1.

Let a=2i+3j+4k and b=3i+4j+5k. Find the angle between them.

Answer»

Magnitudes a=√(2²+3²+4²) =√29, b=√(3²+4²+5²) =√50  

Dot product of these vectors a.b =(2i+3j+4k).(3i+4j+5k) =2.3+3.4+4.5 =6+12+20 =38  

But the value of dot product is also given by abCosθ  

So, abCosθ=38  

Cosθ=38/ab=38/(√29.√50) =38/√1450  

θ=Cos-1(38/√1450)  


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