Find the specified vector or scalar.u = 4i + j and v = 8i + j; Find  | u + v | . Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Write the equation for the plane.The plane through the point P(-7, 5, -4) and normal to n =

Find the center and radius of the sphere.x2 + y2 + z2 – 12x – 14y + 2z = -5 Center:  ( , , ) Radius: 

Identify the type of surface represented by the given equation. + + = 1

Perform the indicated operation.v = -2i – 6j – 3k and w = 2i + 3j + 5kFind  | v | – | w |. Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Identify the type of surface represented by the given equation. + =

Find the corresponding position vector. Define the points P = (7, -6) and Q = (4, -3). Find the position vector corresponding to .

Solve the problem.A force of magnitude 8 pounds pulling on a suitcase makes an angle of 30° with the ground. Express the force in terms of its i and j components.

Find a vector orthogonal to both v and u.v = -3i – 4j + k, u = -4i + 4j + 3k Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  Be sure to use vector notation!  (Either use component form or i, j, k form.) 

Solve the problem.A bullet is fired with a muzzle velocity of 1401 ft/sec from a gun aimed at an angle of 15° above the horizontal. Find the horizontal component of the velocity.