Recall the distance from a point (xo, Yo, zo) to the plane Ax+ By + Cz + D = 0 is given by the formula: |Axo + Byo + Czo + D| VA? + B² + C² Use the method of Lagrange multipliers to find the point on the surface given by x2 +y² + z? = 2z which is closest to the plane given by x +y +z = 3. Hint: Ignoring the absolute value in the formula above, you have a differentiable function in three variables which you are trying to minimize.

Q: Given = (8,−4,1) + t(4, 4, −2), find the point where the line intersects the plane with equation z +…

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Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: satisfies each set of conditions. a) parallel to both the y- and z-axes; contains the point A(-4, 5,…

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Q: Determine the intersection of the two planes: ¹₁:3x + 2y - 6z - 5 = 0 л₂: 2x + 3y9z+10=0

A: We have two equations 3x+2y-6z-5=0 2x+3y-9z+10=0

Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.