Find the length of the perpendicular drawn from the point `(5,4,-1)` . to the line ` vec r= hat i+lambda(2 hat i+9 hat j+5 hat k)dot`

Explanation

`vec {{r}}=hat{1}+lambda(2 hat{1}+9 hat{{j}}+5 hat{{k}})`

`
frac{{x}-1}{2}=frac{{v}-0}{9}=frac{{z}-0}{5}`

`
B :(2 {r}+1,9 {r}, 5 {r})`


Direction ratio of` AB equiv(2 {r}-4,9 {r}-4,5 {r}+1) `

`
2(2 {r}-4)+9(9 {r}-4)+5(5 {r}+1)=0`

`
110 r=39`

`
r=frac{39}{110}`


Length of perpendicular `={AB}=sqrt{(2 {r}-4)^{2}+(9 {r}-4)^{2}+(5 {r}+1)^{2}}`

`
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