How do you find vector parametric equation for the line through the point P=(−4,−5,3) perpendicular to the plane 3x−4y+3z=−1?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the vector parametric equation for the line through the point ( P = (4, 5, 3) ) perpendicular to the plane ( 3x  4y + 3z = 1 ), follow these steps:

Find the normal vector of the given plane. In this case, the coefficients of ( x ), ( y ), and ( z ) in the equation of the plane represent the components of the normal vector. So, the normal vector of the plane is ( \vec{n} = \langle 3, 4, 3 \rangle ).

Let ( \vec{P_0} ) be the position vector of point ( P ), which is ( \vec{P_0} = \langle 4, 5, 3 \rangle ).

Since the line is perpendicular to the plane, the direction of the line must be parallel to the normal vector of the plane. Thus, the direction vector of the line ( \vec{v} ) is the same as the normal vector of the plane, which is ( \vec{v} = \langle 3, 4, 3 \rangle ).

Now, we can write the vector parametric equation of the line using the point ( P ) and the direction vector ( \vec{v} ). It is given by: [ \vec{r}(t) = \vec{P_0} + t\vec{v} ] where ( t ) is a parameter representing any real number.

Substituting the values of ( \vec{P_0} ) and ( \vec{v} ): [ \vec{r}(t) = \langle 4, 5, 3 \rangle + t\langle 3, 4, 3 \rangle ]

Simplify to get the vector parametric equation of the line: [ \vec{r}(t) = \langle 4 + 3t, 5  4t, 3 + 3t \rangle ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 What is the arclength of #(sqrt(e^(t^2)/(e^t)+1),t^3)# on #t in [1,1]#?
 What is the derivative of #f(t) = (e^(t^21)t, t^34t ) #?
 What is the derivative of #f(t) = (t/(t+1) , 1/(t^2t) ) #?
 How do you find the parametric equation of a parabola?
 Given x(t)=3sin(t)  3, y(t)=t1 for 0 is less than or equal to t is less than or equal to 2pi How do you find the velocity of the particle at t=3?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7