Determine a value for k such that the two planes are coincident. -3y+z=-27 -x- 3x+k²y+kz = k* a. k=3 b. k=-2 C. 1 k = d. k = -3 Which of the following is the parametric equation of the line with vector equation r = = (1,2)+5(2,4), s = R? a. x 2t,y 4t, t = R = c. x +1,y=4t+ 2, t = R b. x 4t+2y= 2t+1, € R d. none of the above

Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

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Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

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: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Determine whether the lines L₁ and L2 given by the vector equations are parallel, perpendicular, 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: 16. Let Li be the line with vector equation r (-2,3) + s(-1,3), s e R. Let L2 be the line with…

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Q: A point A(-5,-3) is translated by the vector v = , and then reflected about the line y=0. the…

A: Given that: A(-5, -3) is translated by v=<8, 0>

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

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

Q: Find the position vector (i.e. the direction vector) from the point P(−4,−6,3) to the point…

A: To find the position vector (i.e. the direction vector) from the point  P-4, -6, 3 to the point Q4,…

Q: If a line is parallel to the vector 3i + 9j+ 6k and passes through the point P = (5, 5, 4), then the…

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