Determine the value of k for which these planes are perpendicular. T₁: [x, y, z] = [1 + 4s + kt, 2 + 2s + t, 7 + 21] T₂: [x, y, z]= [0, -3, 3] [4, 1, -1]+s[1, 0, 5] +

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: Let r¡(t) = (-4,0, –5) + t(0, 1, –3) and r2(s) = (2, –2, 10) + s(2,0, 3). Find the point of…

A:

Q: find the point of intersection for the following 3 planes  x–2y+z+6=0 2x+y–z+2=0 2x+y+3z+2=0

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Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

A:

Q: Find the point at which the line r(t) = (7, −7, 4) + t(−6, 6, −8) intersects the az plane.…

A: To find the point where the line intersects xz plane

Q: Let l1 : (x, y, z) = (131, 89, −83) + r (42, 28, −28) where r ∈ R and l2 : (x, y, z) = (29, 21,…

A: LetandShow that the lines  and  are identical.

Q: 11₁ X 4y -6x + 2y = 0, - 6x + 2y = 2, x - 4y = 1, x - 4y = 6 Find S -6x + 2y -dA, where R is the…

A: The Region R is given as , -6x+2y=0 , -6x+2y=2 , x-4y=1 , x-4y=6 find ∫∫R-6x+2yx-4ydA=?

Q: Find an equation for the plane that contains the line v = (-1,2,7) + t(3,2, 4) and is perpendicular…

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Q: Find the equation of the plane parallel to the intersecting lines (1,2-3t, -3-t) and (1+2t, 2+2t,…

A: To find: We have to find the equation of the plane parallel to the intersecting lines 1, 2-3t, -3-t…

Q: J₁ - 6x + 6y Find -6x + 6y 4x + 3y 0, -dA, where R is the parallelogram enclosed by the lines - 6x +…

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Q: 3) Find the distances: a. Between ₁ = (3 + t, −2+ 3t, -t) and 1₂ = (1 + 2t, t, 5+ 4t). b. Between…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step