Find an equation of the plane that passes through the point P(-4, -5, 4) and has the vector n = (-4,9,4) as a normal.

Q: Find a normal vector of the plane that contains the points (1, -2,0). (3, 1, 4) and (0, -1, 2).…

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Q: The plane with normal vector (0, – 2, – 4) containing the point (-7,4,-3) has equation Aæ + By + Cz…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: A normal vector for the plane through the points (2, 5, 1),(3, 7, 0), and (2, 5, 2) is _____ .

A: Given ,            (2,5,1) , (3,7,0), and (2,5,2)

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: What are the components of vector p which has three times the magnitude of the normal vector of the…

A: Given plane: Let the normal vector be n. So,

Q: Find an equation of the plane through the point (2,1,-3) with normal vector 2i-3j+k. Determine the…

A:

Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

Q: | Find a vector equation for the line through the point (–9, –9, 3) parallel to the line 19 + 4t, y…

A:

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find the equation for the plane through the point Po = (3,4,3) and normal to the vector n=21 + 7j +…

A:

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

A:

Q: snip1

A: we have to find the normal and general forms of the equation of the plane that contains the point…

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Give an equation of the plane with a normal vector n = ⟨1, 1, 1⟩ that passes through the point (1,…

A: we know that equation of plane with a normal vector x0,y0,z0 and passes through point x1,y1,z1 is…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

A:

Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +…

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by:…

Q: Find a vector orthogonal to the line x+y=1

A:

Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

A:

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 8 –…

A:

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A:

Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Find an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

A:

Q: Find an equation of the plane. The plane through the point (4, 0, -5) and perpendicular to the…

A:

Q: A normal vector for the plane through the points (2, 5, 1), (3, 7, 0), and (2, 5, 2) is <

A:

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: Write an equation of the plane with normal vector n (7,5, −4) passing through the point (1, −5, 1)…

A:

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: Determine the general equation of the plane that passes through the point P (-1,1,0) and that has a…

A: Plane passing through the point P-1, 1, 0 and has a normal vector n=2, 0, -4.

Q: Find an equation of the plane. The plane through the point (4, 8, 6) and with normal vector 7i + j -…

A: Given, The plane passing through the point (4,8,6) with the normal vector 7i+j-k We know that, The…

Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

A:

Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: write the equation of the line passing through P with normal vector n in (a) normal form and (b)…

A: Given

Q: write the equation of the plane passing through P with normal vector n in (a) normal form and (b)…

A:

Q: Find an equation of the plane with normal vector n =, and contains the line given by the y – 2 z - 6…

A:

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector .

A: topic- equation of plane with point and normal vector

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.