The unit normal vector to the line joining i | vedclass

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(B) Let the points be $A(1, -1)$ and $B(2, 3)$.The vector along the line $AB$ is $\vec{AB} = (2-1)i + (3 - (-1))j = i + 4j$.$A$ vector perpendicular t

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$\frac{-4i + j}{\sqrt{17}}$

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(B) Let the points be $A(1, -1)$ and $B(2, 3)$.The vector along the line $AB$ is $\vec{AB} = (2-1)i + (3 - (-1))j = i + 4j$.$A$ vector perpendicular to $\vec{AB} = i + 4j$ is of the form $\lambda(4i - j)$.The unit normal vector is $\pm \frac{4i - j}{\sqrt{4^2 + (-1)^2}} = \pm \frac{4i - j}{\sqrt{17}}$.The line equation passing through $(1, -1)$ with direction vector $i + 4j$ is $\frac{x-1}{1} = \frac{y+1}{4}$,which simplifies to $4x - y - 5 = 0$.The normal vector to the line $ax + by + c = 0$ is $ai + bj$. Here,the normal vector is $4i - j$.To check the direction towards the origin $(0, 0)$,we test the point $(0, 0)$ in the expression $4x - y - 5$. Since $4(0) - 0 - 5 = -5 Thus,the required unit normal vector is $-\frac{4i - j}{\sqrt{17}} = \frac{-4i + j}{\sqrt{17}}$.

The unit normal vector to the line joining $i - j$ and $2i + 3j$ and pointing towards the origin is

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