Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your answer. ..... Since the V product of the vector parallel to the given line and the normal vector of the given plane is , the line V parallel to the plane.

Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

Q: Find the equation of the plane that contains the point (4, – 1, 3) and is perpendicular to the…

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Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

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Q: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 + 3y + z = 5 Find the normal vector, n,,…

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Q: Is the line x = 6- 3t, y = 8 + 8t, z= -t parallel to the plane 3x + y -z=2? Give reasons for your…

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Q: Find an equation of the plane that passes through the point (0, 0, 0) and is perpendicular to the…

A: The direction ratio of n = −3i + 2k is (-3,0,2) Given that that plane is perpendicular to n = −3i +…

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

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Q: find the acute angle between the given linesby using vectors parallel to the lines. y = x, y = 2x +…

A: Here the acute angle between two lines is to be calculated.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 4t, y = 4 –…

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Q: Show that the vector v = [a, b, c]* is perpendicular to the plane P with equation ax + by + cz + d =…

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Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A: Let's find.

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 a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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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: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

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 –…

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

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: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: What is a vector that is normal to the plane 4x+6(y-100)+7(z-200)=20? O A. 4i+6j-20 k O B. 8i+ 12 j…

A: Given query is to find the normal vector.

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

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

A: We will use that if Ax+By+Cz=d is equation of plan than (A,B,C) is normal vector as well as…

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Is it possible to find a plane perpendicular to both i and j? Explain why.

A: The objective is to find a plane perpendicular to both i and j, if possible.

Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

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: Suppose that n is normal to a plane and that v is parallel to the plane. Describe how you would find…

A: Consider the given information as n is normal to a plane and that v is parallel to theplane.

Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5 +t and L2: x = 1+4t, y = 3 – 8t, z = 5 – 4t are…

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Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

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

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Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

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

A: Solution is given below:

Q: By vector methods find the angle between the line x = y = 2z and the plane x + y + z = 0.

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Q: Given the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (a) Find a vector…

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Q: The planes 3x−4y+5z=−28 and 4x−2y+4z=−24 are not parallel, so they must intersect along a line that…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 5 -…

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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: Consider the lines : = 2z - 6 and m : x = −1+10t, y = 7t, z = 2+t. 5 7 1. Determine if & and m are…

A: This is a question of Vector Algebra.

Q: Verify that the two planes are parallel. -x + 6y + 3z = 5 -** 1 -x+ 2y + z = 6 Find the normal…

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Q: The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y)…

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