Questions from General Calculus

Q: Find the point at which the line intersects the given plane.

Find the point at which the line intersects the given plane. x = t - 1, y = 1 + 2t, z = 3 - t; 3x - y + 2z = 5

Q: Differentiate. y = secθ  tanθ 

Differentiate. y = secθ  tanθ 

Q: Where does the line through (-3, 1, 0)

Where does the line through (-3, 1, 0) and (-1, 5, 6) intersect the plane 2x + y - z = -2?

Q: Find equations of both lines that are tangent to the curve y

Find equations of both lines that are tangent to the curve y = x3 – 3x2 + 3x -3 and are parallel to the line 3x – y = 15.

Q: Find direction numbers for the line of intersection of the planes x

Find direction numbers for the line of intersection of the planes x + y + z = 1 and x + z = 0.

Q: Determine whether the planes are parallel, perpendicular, or neither.

Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.) x + 4y - 3z = 1, 23x + 6y + 7z = 0

Q: Determine whether the planes are parallel, perpendicular, or neither.

Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.) x + 2y - z = 2, 2x - 2y + z = 1

Q: (a). Find parametric equations for the line of intersection of

(a). Find parametric equations for the line of intersection of the planes and (b). find the angle between the planes. x + y + z = 1, x + 2y + 2z = 1

Q: (a). Find parametric equations for the line of intersection of

(a). Find parametric equations for the line of intersection of the planes and (b). find the angle between the planes. 3x - 2y + z = 1, 2x + y - 3z = 3

Q: Find symmetric equations for the line of intersection of the planes.

Find symmetric equations for the line of intersection of the planes. 5x - 2y - 2z = 1, 4x + y + z = 6