For problems 6 and 7, use the points P(-3, 4,2), Q(-1,6, 2), R(5,3, -1) 6. Find a vector perpendicular to the plane formed by P, Q and R. 7. Find the distance from P to the line through Q and R.

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: 28. In the standard (x, y) coordinate plane, the point (2,-6) is the midpoint of the line segment…

A: Given,  In the standard x,y coordinate planeThe point  2,-6  is the midpoint of the line segmentwith…

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: Prove that the equation 2x²+3xy - 2y-x+3y -1= 0 represents a pair of perpendicular lines.

A: Given that: 2x2+3xy-2y2-x+3y-1=0

Q: Do the points (0.5, 1), (1, 1.2), (2, 2) lie on a line?

A: Three points will lie on same line if slope of any two point is same as other two points, taken two…

Q: If line 3x-ay-1=0 then find the values of a. is parallel to the line (a +2) x-y+3=0

A: Given that the line is parallel to the line .We have to find the value of a .

Q: Which of the following lines is parallel to (3 + 4t,-2 5t) ? 3x +2y = 7 %3D -3x - 2y = 4 O 4x 5y = 6…

A: Given a line in parametric form, 3+4t, -2-5t. This can be written as: x-34=y+2-5 which on further…

Q: Match each line with a perpendicular line. A. y = 5x +2 1. the line through (2, 12) and (17, 9) В.…

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Q: 257. Show that the line passing through points P(3, 1, 0) and Q(1, 4, -3) is perpendicular to the…

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Q: The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 +…

A: The given lines r→=j^+t4i^+2j^+3k^R→=-i^-7j^-12k^+si^+2j^+3k^ Let,  4i^+2j^+3k^=b1→i^+2j^+3k^=b2→ As…

Q: 4. Find the equation of line 4 that is parallel to v=-i+3j+2k and goes through the point (-6,20,1).…

A: Answer is mentioned below

Q: Find the equation of a line through the coordinate (3,- 2) and parallel to the line represented y =

A: y = (1/2)x -2   ...i Equation of line parallel to ....i is  y= (1/2)x + c ( where c is constant) If…

Q: Which of the lines x – y + 3 = 0 and x – 4y –7= 0 is father from the origin? -

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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: The perpendicular distance from (5,3) to the line y+4x= 6

A: Line = y+4x-6 = 0 and point ( 5,3)We Know that the perpendicular distance d= ax + by +ca2+b2Where a…

Q: The line perpendicular to y = -2x + 1 that passes through (1,3) is   subject: straight and…

A: The answer is found in step-2

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: Consider the lines r(t) = (2-3, +4--1) and r(s) (+4,- +3,3+6). A. Show that these two lines…

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