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#6 {main}</pre> and straight B with rightwards arrow on top space equals space 2 straight i with hat on top plus straight j with hat on top minus 4 straight k with hat on top?


Given that,

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#6 {main}</pre>

and      straight B with rightwards arrow on top space equals space 2 straight i with hat on top plus straight j with hat on top minus 4 straight k with hat on top

Let straight theta be the angle between the given two vectors.

We know,  straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space AB space cos space straight theta

∴               cos space straight theta space equals space fraction numerator straight A with rightwards arrow on top times straight B with rightwards arrow on top over denominator AB end fraction

Now           straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space left parenthesis straight i with hat on top minus 2 straight j with hat on top minus 5 straight k with hat on top right parenthesis. left parenthesis 2 straight i with hat on top plus straight j with hat on top minus 4 straight k with hat on top right parenthesis

                         equals space 2 minus 2 plus 20 space equals space 20

Magnitude is given by,

 open vertical bar straight A with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 5 right parenthesis squared end root space equals space square root of 30

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#6 {main}</pre>

 Thus, angle between the vectors,

 cosθ space equals space fraction numerator straight A with rightwards arrow on top times straight B with rightwards arrow on top over denominator AB end fraction equals fraction numerator 20 over denominator square root of 30 cross times square root of 21 end fraction equals square root of 40 over 63 end root

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#6 {main}</pre>    

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