find the measure of acute angle between the vectors whose direction ratio are 4,2,3 and 1,2,4

Dear Student,
Please find below the solution to the asked query:

We havea=4i^+2j^+3k^b=i^+2j^+4k^If θ is required acute angle, thencosθ=a·bab=4i^+2j^+3k^.i^+2j^+4k^16+4+91+4+16=4+4+122921=202921θ=cos-1202921

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