Four students each made a statement about the equation of a line in R² given in vector form, 7 = (-3,5) + t(2,-3). Which students is/are correct? Justify your answer. i. Eleven: The equation of this line in scalar form is 2x + 3y - 1 = 0 ii. Lucas: A line L, that is parallel to the given line is as follows: (x = 1+ 2.5t L: y=8-3.75t iii. Finn: A vector that is perpendicular to the given line is v = (9,-4) iv. Dustin: Two points on this line are: (-1,2) and (0,0.5)

Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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Q: - - 1. If à = 2ảx + 6ảy – 3ả₂ and ☎ = −3ảx – 4ảy – 5ả₂, find a. a unit vector in the direction of A…

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Q: Determine whether the following lines in R2 represented by the vector equations below intersect, are…

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Given u = , v = -5i - j, and w (AB) is defined by the points (1, 6) and (-2, 8). a Find v in…

A: This is  a problem of vector. By dissolving vector in x and y parts we will convert it into…

Q: O ich of the following is a vector equation for the line through (-1,2,-2) and parallel

A: We have to find the vector equation for the line through (-1,2,-2)and parallel to…

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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Q: Solve the problem. Find the area of the triangle determined by the points P(-3, 6, -4), Q( 2, 10,…

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Q: When - - [B] - [12] u= V then the vectors in Span{u, v} lie on a line through the origin. True or…

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Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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Q: Find the equation of the line L that passes throught point P ( – 4, 3, 7) and Q( – 8, 1, − 5). Enter…

A: r(t)=<-4,3,7>+t<-4, -2,-12>Explanation:Hope it helps youplease ask if you have any…

Q: an example of a (nonzero) vector perpendicular to ?⃗ = ⟨−17, 3, −6⟩. Please give full explanation…

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Q: Solve the problem. 1. Find the symmetric equations for the line through the point P(5, -3, -5)…

A: Given that The point Px1, y1, z1=5,-3,-5The vector  =-6i+7j-7ka,b,c=-6,7,-7

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

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Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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