2. Let v be a vector parallel to a line that passing through the points P(1,0,-3) and Q(3,3,-3). a. Find the equation of the plane that passing through P and has v as its normal vector. b. Find the distance of that plane to the Q.

Q: Find the coordinates of a point P on the line and a vector v parallel to the x - 7 y + 9 = z + 4…

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Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope…

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

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A: Here the given equation of the straight line is x-28=y+57=z+7  -----(i) We have to find the…

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A: Find your answer below

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Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

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

A: Given: (4, −1, 5

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: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Which of the following describes a plane perpendicular to the vector n = (2, 1, -4) and contains the…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. X - 8 y + 2 = z +…

A: This question is based on 3-d coordinate geometry.

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A: n=-3i-4j+4k  and P(2,-7,5)

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given: (2,3,-6) Perpendicular to j vector

Q: a. Which translation vector represents the path of the ball from T tol DC? DC? b. What translation…

A: GIVEN :

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

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 2 %3D y + 5 =…

A: The given question has been solved in detail.

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A: Explanation of the answer is as follows

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

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

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 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,…

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A: First obtain a, where a is the distance between R0 and Q.

Q: a) The line y =- 5x + 9, in VECTOR form (R?).

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Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

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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: Let / be the line through the point with coordinates (-1,-2,-1) in the direction of the vector Which…

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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 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: Find the vector and the cartesian equations of the plane containing the point î+ 2j – k and parallel…

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Q: Consider the lines 3 - z x – 5 l1 : 2 and I. Find two unit vectors that are parallel to l1.

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Q: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

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Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector