Questions from General Calculus

Q: Find the distance from the origin to the line x = 1

Find the distance from the origin to the line x = 1 + t, y = 2 - t, z = 21 + 2t.

Q: Determine whether the lines given by the symmetric equations /

Determine whether the lines given by the symmetric equations are parallel, skew, or intersecting.

Q: The height (in meters) of a projectile shot vertically upward

The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 24.5 m/s is h = 2 + 24.5t - 4.9t2 after t seconds. (a) Find the velocity a...

Q: Find an equation of the plane through the line of intersection of

Find an equation of the plane through the line of intersection of the planes x - z = 1 and y + 2z = 3 and perpendicular to the plane x + y - 2z = 1.

Q: (a). Find an equation of the plane that passes through

(a). Find an equation of the plane that passes through the points A (2, 1, 1), B (-1, -1, 10), and C (1, 3, -4). (b). Find symmetric equations for the line through B that is perpendicular to the plane...

Q: An ellipsoid is created by rotating the ellipse 4x2 + y2 –

An ellipsoid is created by rotating the ellipse 4x2 + y2 – 16 about the x-axis. Find an equation of the ellipsoid.

Q: (a). Find an equation of the sphere that passes through

(a). Find an equation of the sphere that passes through the point (6, -2, 3) and has center (-1, 2, 1). (b). Find the curve in which this sphere intersects the yz-plane. (c). Find the center and radiu...

Q: Differentiate the function. f (x) = ln (

Differentiate the function. f (x) = ln (1/x)

Q: Calculate the given quantity if a = i + j -

Calculate the given quantity if a = i + j - 2k b = 3i - 2j + k c = j - 5k (a). 2a + 3b (b). |b | (c). a ∙ b (d). a × b (e). |b × c | (f). a ∙ (b × c) (g). c × c (h). a × (b × c) (i). compa b (j)....

Q: Find the highest and lowest points on the curve x2 + xy

Find the highest and lowest points on the curve x2 + xy + y2 = 12.