Calculus 8th Edition

(a) Find two vectors between the three points $P,Q$ and $R$ , for example find $\vec{PQ}$ and $\vec{QR}$ and see if they are parallel that is, scalar multiples of each other. If they are parallel , then the points are on the same line , otherwise they are not. (b) Take three points such as $P,Q,R$ to find two vectors ${PQ}$ and ${QR}$. Take the cross product of ${PQ} \times {QR}$to find the normal vector $\lt a,b,c \gt$ Let $P,Q,R$ as $(x_0,y_0,_0)$ be a point on plane equation: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$ Three points always lie in a single plane, so we only need to test the 4th point $S$ in the resulting plane equation to see the numbers work.If they do then all four points lie in the same plane.
(a) Find two vectors between the three points $P,Q$ and $R$ , for example find $\vec{PQ}$ and $\vec{QR}$ and see if they are parallel that is, scalar multiples of each other. If they are parallel , then the points are on the same line , otherwise they are not. (b) Take three points such as $P,Q,R$ to find two vectors ${PQ}$ and ${QR}$. Take the cross product of ${PQ} \times {QR}$to find the normal vector $\lt a,b,c \gt$ Let $P,Q,R$ as $(x_0,y_0,_0)$ be a point on plane equation: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$ Three points always lie in a single plane, so we only need to test the 4th point $S$ in the resulting plane equation to see the numbers work.If they do then all four points lie in the same plane.