arrow_back How do I determine the equation of a normal in $R^2$ or $R^3$?

11 views
How do I determine the equation of a normal in $R^2$ or $R^3$?

(a) If $a$ and $b$ are constants that are not both zero, then an equation of the form $$a x+b y+c=0$$ represents a line in $R^{2}$ with normal $\mathbf{n}=(a, b) .$

(b) If $a, b$, and $c$ are constants that are not all zero, then an equation of the form $$a x+b y+c z+d=0$$ represents a plane in $R^{3}$ with normal $\mathbf{n}=(a, b, c)$.
by Platinum
(106,844 points)

Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find an equation of the hyperplane $H$ in $\mathbf{R}^{4}$ that passes through the point $P(1,3,-4,2)$ and is normal to the vector $u=[4,-2,5,6]$.
Find an equation of the hyperplane $H$ in $\mathbf{R}^{4}$ that passes through the point $P(1,3,-4,2)$ and is normal to the vector $u=[4,-2,5,6]$.Find an equation of the hyperplane $H$ in $\mathbf{R}^{4}$ that passes through the point $P(1,3,-4,2)$ and is normal to the vector $u=4,-2,5,6$. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Determine the remainder by using the remainder theorem. $f(r)=-5 r^{3}+8 r^{2}-4 r-7 ; g(r)=r+3$
Determine the remainder by using the remainder theorem. $f(r)=-5 r^{3}+8 r^{2}-4 r-7 ; g(r)=r+3$Determine the remainder by using the remainder theorem. $f(r)=-5 r^{3}+8 r^{2}-4 r-7 ; g(r)=r+3$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
$-\frac{3}{4}$ is a root of the equation $0=12 y^{2}-7 y+c$. Determine the value of $c$ and the other root.
$-\frac{3}{4}$ is a root of the equation $0=12 y^{2}-7 y+c$. Determine the value of $c$ and the other root.$-\frac{3}{4}$ is a root of the equation $0=12 y^{2}-7 y+c$. Determine the value of $c$ and the other root. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Determine the equation of the circle with centre $(-2 ;-1)$ through the point $(5 ; 1)$.
Determine the equation of the circle with centre $(-2 ;-1)$ through the point $(5 ; 1)$.Determine the equation of the circle with centre $(-2 ;-1)$ through the point $(5 ; 1)$. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Determine the equation of the circle with centre $(-3 ; 3)$ through the point $(5 ; 1)$.
Determine the equation of the circle with centre $(-3 ; 3)$ through the point $(5 ; 1)$.Determine the equation of the circle with centre $(-3 ; 3)$ through the point $(5 ; 1)$. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Determine the equation of the circle with centre $(5 ;-3)$ through the point $(3 ; 2)$.
Determine the equation of the circle with centre $(5 ;-3)$ through the point $(3 ; 2)$.Determine the equation of the circle with centre $(5 ;-3)$ through the point $(3 ; 2)$. ...
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$ ...