For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction vector for the line.

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: In Cartesian space, the direction of the line (x, y, z) = (a, b, c) +r(d, e, f) is represented by…

A: The given line is (x,y,z)=(a,b,c)+r(d,e,f) So, the point (a,b,c) is on the line and (d,e,f) is a…

Q: Determine the value of k for which the direction vectors of the lines x+3 Z = y = -1 are…

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Q: Find the point at which the line intersects the given plane.

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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…

A: Let's find.

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: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

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Q: Use vectors to show that the distance from P1(x1, y1) to the line ax + by = c is d = |ax1 + by1 -…

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

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Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Q: Consider these lines, where s,t, E R 11: [x, y, z] = [2, 1, -4] + t[1, 3, 1] 12: [x, y, z] = [1, k,…

A: Two lines are said to be coplanar if they lies in same plane. The equation of line passing through…

Q: Determine whether the plane x + y + z = 9 and the line x = t, y = t + 1, z = t + 2 are parallel,…

A: Given: The planes x + y + z = 9 and the line x = t, y = t + 1 , z = t + 2.   To determine Whether…

Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

Q: Suppose L1 and L2 are disjoint (nonintersecting) nonparallel lines. Is it possible for a nonzero…

A: Given:

Q: Forces are called concurrent when their lines of action meet in Perpendicular planes Select one:…

A: Given the statement Forces are called concurrent when their lines of action meet in perpendicular…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(0, 0, 0) P2(2, -2,…

A: To find:(a) the direction of vector P1P2(b) the midpoint of line segment P1P2P1(0,0,0) and…

Q: Find the direction vector of the line of intersection of the planes x + 2y +z = O and x+y+1 = 0. %3D

A: Line of intersection of two planes

Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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Q: Show that the lines x = p + su and x = q + tv are skew lines. Find vector equations of a pair of…

A: Consider the matrix values given. The equation can be written as :

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: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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

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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: Show that the lines L1 : x =1- t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

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Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: a) Find the vector that is parallel to the tanget to the circle x2 + y2 = 100 at the point (3,-4).…

A: a) Given equation of circle, x2 + y2 = 100. We have to find the vector equation which is parallel to…

Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

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: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,…

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

Q: Show that the lines L1 : x = 2 – t, y = 2t, z =1+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

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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…

A:

Q: Show that the lines L1 : x = 3 – t, y = 2t, z = 3+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

A:

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

A: Let's find.

Q: Determine the way in which the line [x, y, z] = [2, −3, 0] + k[−1, 3, −1] intersects the plane [x,…

A: Here given as x, y, z=2, -3, 0+k-1, 3, -1⇒x=2-k⇒y=-3+3k⇒z=-k .......1 Thus the equation of the line,…

Q: Show that direction vectors of the lines L: and are arthogonal.

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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: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

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

A: To show that the lines L1: x=4-t, y=2t, z=5+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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Q: Let Q be a point in R°. Consider a line passing through P with direction vector d.What is the…

A: We are asked to find the distance from a point Q in ℝ3 to the line which passes through a point P…

Q: Let Q be a point in R°. Consider a line passing through P with direction vector d. What is the…

A: Please check image in step 2