1. The two unit vectors parallel to the line y 5x + 2 are and 2. The two unit vectors parallel to the line 2x + 5y = 1 are and 3. The two unit vectors perpendicular to the line y = x – 4 are and

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: In each part, find the two unit vectors in R² that satisfy the given conditions. (1) The two unit…

A: A vector which passes through any two distinct points of a line is parallel to that line.

Q: Q3:If the two vectors A= 3i +2j + 5k, and B= 2i - j+4k, they located in the x and y plane, find the…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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: 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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Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

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: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: If a line is parallel to the vector 2i + 7j + 10k and passes through the point P = (6, 10, 5), then…

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Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: Given query is to find the point and the parallel vector.

Q: A given line is described by x+2y = 4. Vector A starts at the origin and ends at point P on the line…

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Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: topic - point and vector parallel to line

Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

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Q: The lines L₁ and L2 meet at the point P. The line L3 is coplanar with L₁ and L2 and is perpendicular…

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Q: Suppose a line is given parametrically by the equation L(t) = (-4t, –4 – 3t, 4 + 4t) Then the vector…

A: topic - equation of line

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: In each part, find the two unit vectors in R2 that satisfy the given conditions.   The two unit…

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Q: In each part, find the two unit vectors in R² that satisfy the given conditions. 1. The two unit…

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Q: 3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i+ j – k Answer + (2i+ 2.4j…

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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: 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.

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: 1. Give the vector equation of a line perpendicular to the line L: x= 21-1, y=-31, 1 e R. Are there…

A: Given line: l:x=2t-1, y=-3t, t∈ℝ To find the other line The vector equation of the line is…

Q: Which one of the following vectors is perpendicular to the line L: 2x +3y- 6= 0 O 2i- 3j O 21 3j

A: concept:  a line ax+by=c has perpendicular vector <a,b>

Q: If the line through the point (3,-4,-1) and parallel to the vector i+j+k. The equation of the line…

A: We can answer the question as false or true as below

Q: Find a vector perpendicular to the lines: 4₁: x = 3-4t y=-2-6t x = -1 + 2t y=4-t L₂: O O None of…

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Q: Consider the lines e: =2- y = z +1 and l2: , = y - 2 = 3 1. Determine a direction ve ctors for the…

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Q: B) find a vector that is parallel to the line whose equation is : 4-x 3-6z % = 3 – 3y = 5 9

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Q: ) Write down the position vectors of any two points on the line T·(3i – 4j)+ 2 = 0 and hence find…

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Q: Let L be the line 8x + 2 in R?. Find vectors a and b so that v a + tb with t ER is also a correct…

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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: 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: 27. Are the points P(1, 2), e(7,3), and R(-2, 1) on the line with vector equation = (19,5) + s(6,1),…

A: According to our terms and conditions I have solved first question for next question repost

Q: Owing vectors is perpendicular to the line L: 2x +3y- 6 = 0 2i + 3j O 2i - 3j (후 +1를 이 rious

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Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: 1. The two unit vectors parallel to the line y = 2x 1 are | and 2. The two unit vectors parallel to…

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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 the equation of the line that goes through the point A = (5, –3, –4) and is parallel to the…

A: Given that the line passes through the point A=5,-3,-4 and is parallel to the vector  v=-2,4,3 The…

Q: Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is…

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Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

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: 19. Find the angle between the line and the plane of the following equations, X_ y- 2_ 3z+ 3 b. L:…

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Q: Find an equation for the line through P(11,10) parallel to vector v=2i-3j

A: Given point on the line is P(11,10) The vector parallel to the line is,v=2i-3j

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: 14. Given that a and bare two vectors, then the vector (a + b) × (a – b) is A. perpendicular to (a –…

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Q: (7) Find the angles between the following lines (a) r =i – 2j + (i – j) and r = 2i – 6j + µ(i – 2j);…

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