A line L has a direction vector v =i+3j+ V6k and passes through the point Q. Find the distance between a point P and the line Lif IQP x v = 16

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

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Q: Show that direction vectors of the lines Le and are orthogonal.

A: Given lines are  L1=x-32=y+14=z-2-1L2=x-35=y+1-2=z-32 To prove the directional vectors of these two…

Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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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: 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: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

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

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

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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 direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

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: A line L has a direction vector v = 2i + 4j + V5k and passes through the point Q %3D Find the…

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

A: Given:

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.

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

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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 v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

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Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: By vector methods, show that the line segment joining the midpoints of two sides of a triangle is…

A: To prove :- The line segment joining the midpoints of two sides of a triangle is parallel to the…

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: find the length and direction (when defined) ofu * v and v * u. u = 2i, v = -3j

A: Given vectors: u=2i+0j+0k and v=0i-3j+0k u×v=ijk2000-30u×v=i0×0-0×-3-j2×0-0×0+k2×-3-0×0u×v=-6k The…

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

A: We have, L1: x=4-t, y=2t, z=2+t and L2: x=1+4t, y=3-8t, z=5-4t

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

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

Q: A line L has a direction vector y = i+ 3j+ v6k and passes through the point Q Find the distance…

A: We have to solve given problem:

Q: 2. Given two non-parallel lines l1: r = 2+t, y = 4+t, z = 8, and l2: x = 3, y = 2 + t, z = 5+t, (a)…

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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 = 5+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t 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…

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Q: Define the line Lo to be a = xo + at, y = yo + bt, z = z0 + ct. If Lo passes through the origin,…

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Q: Give the vector equation of the line passing through P and Q

A: Consider the points: P=1, -2Q=3, 0

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

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Q: Let / be the line through the point with coordinates (-1,2,0) in the direction of the vector Which…

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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: A line L has a direction vector v = i+ 3j+ V6k and passes through the point Q. Find the distance…

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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

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.