MTH Exam 2 Problems

Find the distance between and midpoint of the line segment of  the two points

Write equation of the sphere centered at (2, 0, -1) with radius 3.

Find center and radius of the sphere

Show that the vectors are equal

Find the magnitude/length/norm of the following vectors

Let u = <2,-3,5>, v= <-1,-3-5>. Find

Determine the location of a point (x,y,z) that satisfies the conditions

Find the distance between the points

Find the coordinates of the midpoint of the line segment joining the points

Complete the square to write the equation of the sphere in standard form. Find the center and radius

Find the component form and magnitude of the vector v with the given initial and terminal points. Then find a unit vector in the direction of v

Find each scalar multiple of v and sketch its graph

Find the vector z given that u = 〈1, 2, 3〉, v = 〈2, 2, −1〉, and w = 〈4, 0, −4〉.

Find the magnitude of v

find a unit vector (a) in the direction of v and (b) in the direction opposite of v.

Check if the following vectors are unit vectors, if not make them unit vectors

Write the following vector as a linear combination of standard unit vectors

Find terminal point of v=2i+3j+0k with initial point (2,1,1) 

Find Dot/Scalar/Inner Product of

Find angle between the following two vectors

Perform the following vector operations on the given vectors

find the angle θ between the vectors (a) in radians and (b) in degrees

use the alternative form of the dot product to find

determine whether u and v are orthogonal, parallel or neither

(a) find the projection of u onto v and (b) find the vector component of u orthogonal to v

Prove the following dot product properties

Find the determinant of

Find the cross product of

Write equation of the line 

Determine if the following lines intersect

Find the cross product of the unit vectors and sketch your results

Find u x v and show that it’s orthogonal to both

Find a unit vector that is orthogonal to both u and v

Find the area of a parallelogram that has the given vectors as adjacent sides. Use a graphing utility to verify your results

Find the area of a triangle with the given vertices. (Hint: 1/2||u x v || is the area of a triangle having u and v as adjacent sides

Determine whether each point lies on the line

Find a set of parametric equations of the line with the given characteristics.

Determine whether the lines intersect, and if so, find the point of intersection and the angle between the lines

Determine whether each point lies in the plane

Find an equation of the plane with the given characteristics.

Determine whether the planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle between the planes.

Write the equation of a plane given

Write the equation of a plane given

Find cos(a)

Find the line of intersection for the following

Find the equation of the plane passing through the point

Find equation of the plane R passing through the points

Find a set of parametric equations of the line with the given characteristics.