Which of the following planes is normal to the line given as: x = 2t + 3, y = 5t - 7, z = t - 4 O a. O b. O C. O d. 2x + 5y + z = 12 2tx + 5ty + t = 0 5x - 2y = 0 3x - 7y4z = 14

Q: a. 7 = (3, 1) + (-3, 5), te R b. x = -6 + 2s and y = 3 - 2s, se R Two lines L₁ = (5, 3) + p(-4, 7),…

A: The given lines are:L1​:  r=⟨5,3⟩+p⟨−4,7⟩,    p∈RL2​:  r=⟨5,3⟩+q⟨2,1⟩,    q∈R Both lines intersect…

Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: 18. Find the points of intersection of the lines 4₁: R= 2i + 3j + 3k + t(i-2j + 5k) y +1 2 12: x + 3…

A: These two line not intersect

Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

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Q: 1. The line y - 6 = 2(x + 4) passes through which point? OA (-4,-6) O B. (4, −6) Oc( 4, 6) OD (2,6)

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Q: 9. Find the equation for the plane through Po(-2,3,9) perpendicular to the line x = -2 – t, y = -3 +…

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Q: Guide Plot. label and connect the following coordinates F (-5, -4), G (-2, 4) & H (3, -4) on the…

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Q: . Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find x and y if (2, 5) is the midpoint of points (x, y) and (-5, 6). b. Find the point (0, y) that…

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Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: Determine whether the following two lines L1 and L2 are parallel, interesecting, or skew. L1: x/2 =…

A: Solve the following

Q: 16/22 What is the value of y = -0.4x+ 12 when When x= -4, the value of y is x= -4?

A: We find the value of y when x = -4. y = -0.4x + 12

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and…

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Q: This table gives a few (, y) pairs of a line in the coordinate plane. -38 40 -23 30 -8 20 What is…

A: To find the x-intercept first we have to find the equation of line that passes through these point…

Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: You have three lines: LI: x = 3 + 2s, y = -1+4s, z 2-s L2: x = 3+ 2t, y 2 +t, z=-2+ 2t L3: x = 1+ 4u…

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Q: 2. Which point is the intersection of x + 2y = 8 and 2x + 3y = 10? a. (-2, 5) %3D b. (-4, 6) с. (2,…

A: The given equations are x+2y=8          …12x+3y=10      …2

Q: Which of the following ordered pairs satisfy the 7x+8y0? а. (1,-5) b. (5,-1) . с. (1,1) • d. (0,0)

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Q: Find the line of intersection between the lines: +1 and +.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Are the following lines parallel, intersect at a point, or skew? x = 4-3t y = 2+5t z = -2+t ----- x…

A: The objective of this question is to determine the relationship between two given lines in…

Q: Determine if the lines ℓ1: x − 9 = −t, y + 4 = 3t, z − 9 = 3t and ℓ2: x − 1 = s, y − 4 = −s, z − 9…

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Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

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