Let and be planes in R with, respectively, normal equations 4x +2y-z=-12 and -...

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Let ₁ and ₂ be planes in R³ with, respectively, normal equations 4x +2y-z=-12 and - 3x - 4y + 5z = 25. a. The planes and we are not parallel, so they must intersect along a line which is common to both of them. Find a parametric vector representation of this line. Answer: (Use 't' (without the quotes) as the parameter in your representation.) b. Find a normal equation of the plane which contains the origin and is orthogonal to both and 2. Answer: (Use 'x', 'y' and 'z' (without the quotes) as the variables in your equation.) c. Find a normal equation of the plane which contains the point (3, 3, 1) and is orthogonal to both ₁ and 2. Answer: (Use 'x', 'y' and 'z' (without the quotes) as the variables in your equation.) d. Find a parametric vector representation of the line which contains the point (3, 3, 1) and is parallel to both w and ₂. Answer: (Use 't' (without the quotes) as the parameter in your representation.) Let ₁ and ₂ be planes in R³ with, respectively, normal equations 4x +2y-z=-12 and - 3x - 4y + 5z = 25. a. The planes and we are not parallel, so they must intersect along a line which is common to both of them. Find a parametric vector representation of this line. Answer: (Use 't' (without the quotes) as the parameter in your representation.) b. Find a normal equation of the plane which contains the origin and is orthogonal to both and 2. Answer: (Use 'x', 'y' and 'z' (without the quotes) as the variables in your equation.) c. Find a normal equation of the plane which contains the point (3, 3, 1) and is orthogonal to both ₁ and 2. Answer: (Use 'x', 'y' and 'z' (without the quotes) as the variables in your equation.) d. Find a parametric vector representation of the line which contains the point (3, 3, 1) and is parallel to both w and ₂. Answer: (Use 't' (without the quotes) as the parameter in your representation.)