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

Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 8 1. x + 2y + z = 9 Find the normal vector,…

A: Let's find.

Q: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: Find the vector equation for the line of intersection of the planes x + 4y + z = -5 and x + 4z = 0…

A: Here we have to find the vector equation for the line of intersection of the planes x+4y+z = -5 and…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z = -13. Find the following. 1. A vector…

A: The given planes are: x-10y-2z=3 and 2x-y+z=-13 Let us assume z=t on the line of intersection, where…

Q: What is equation of the plane passing through the point A(-2, –1, –3) and parallel to the vectors ā…

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: Consider the following lines: 4:z=1,y-1=-4,2=1-3t :z=2s+1,y=1-3s,z=1 y+1 z-1 2a Find the…

A: Explanation of the answer is as follows

Q: 10. Consider the plane P given by r + y – 3z = 0. (a) Find the projection of the vector (2, 1, 0)…

A: Given plane : x+y-3z=0  Projection of A along B is A.B/|B|

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 3 and…

A: Given plane equations are  x + y + z = 3 and x + z = 0. We have to find the intersection line…

Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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Q: Q The unit vector normal to the plane 2x + 3y+ 6z = 7 is (2ax +3ay +6 az)/7 (2ax - 3ay-6 az)/7 (4ax…

A: The given plane equation is 2x+3y+6z=7. The unit vector normal to the plane ax+by+cz=d is…

Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Define a basis B = (ā,b, c) for R³, where -- 2 6= 1 3 Define P to be the plane spanned by d and b.…

A: To define a basis B=a→, b→, c→, we determine the determinant of matrix formed by vectors a→, b→, c→.…

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: Find a unit vector normal to the plane containing v=i+3j-2k and w=-2i+j+3k.

A: There are two types of quantities that exist in nature, one is scalar quantity and the other one is…

Q: Consider a plane in space that passes through the point (1, 3, 4) whose normal vector n is a…

A: The direction vector of given line is Therefore, normal vector to given plane is  We know that…

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

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z 2x2 + y and…

A: z=2x2+y2  & x=ey We can see that y can be represented in terms of x.

Q: Find x such that the vectors xi+2j -3k, i+j ,j+3k are Coplanars (lies the Same Plane) . on

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Q: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

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Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

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Q: 3. Complete the following questions using the following planes T₂: 2x+4y-6z-2=0 m₂: 7x+14y-21z-7=0…

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Q: Let S be the plane defined by 5x-Sy+10z 0, and let T be the plane defined by 2x-2y+5z=-2. Find the…

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Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is…

A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the…

Q: Find a vector tangent to the curve of intersection of the two cyclinders ? + y² = 98 and y² + z² =…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

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

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Q: Show that the vector V = (x+ 3y)i + (y – 32) j+(x – 2z)k is solenoidal. %3D

A: Solenoidal Vector : A vector function whose divergence vanished identically is called a solenoidal…

Q: Find a vector parameterization of the plane −5x−4y−5z=18. r(s,t)=_____? (Use s and t for the…

A: A parametrization for a plane can be written as                                       r = s a + t b…

Q: a) Find the distance between two skew lines L1 and L2 such that L1: 1+ 4t, y=5-4t, z=-1+5t  L2:…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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

A: The normal form of the equation of a plane P in ℝ3 is  n.x-p = 0  or  n.x = n.p where p is a…

Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: 9. Find the normal unit vector n to the surface 62 + 2y²+ 2² = 225 at the point P: (5,5, 5).

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Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 1 2t x + 3y + z = 7 Find the normal…

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Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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Q: Find a vector parallel to the line of intersection of the planes 4х + 2y - 33 %3D17 and 3x - 4y…

A: Vector parallel to the Inter section of two planes  a and b is cross product of a and b Let m is a…