Calculus 3 FINAL EXAM

What is the parametric equation for the path of a car moving through the point (-2,0,4) with a velocity vector of v=2i+4+-2k?

• r(t) = (-2+2t, 4t, 4-2t)

• r(t) = (-2+2t, 4t, 4+2t)

• r(t) = (-2-2t, 4t, 4-2t)

• r(t) = (-2+2t, 4t, 4+2t)

Imagine two carpenters working together to build a house. One carpenter uses a specific technique to combine the force and direction of their hammer swings, resulting in a new combined force and direction.

• Cross Product

• Dot Product

• Scalar

• Vector Product

Find the parametric equation of the line segment between the points P(2,1,4) and Q(3,-1,3)

• r(t) = (2+t, 1-2t, 4-t)
• r(t) = (2-t, 1-2t, 4-t)
• r(t) = (2+t, 1-2t, 4+t)
• r(t) = (2-t, 1+2t, 4+t)

In a physics class, the result of multiplying two non-zero parallel or anti-parallel vectors is always equal to the _____ vector

• negative

• orthogonal

• zero

• non-zero

When Ava and Liam are working on a construction project, and the force vectors a and b are perpendicular to each other, what is the magnitude of the cross product?

(a)  

To demonstrate that the forces are perpendicular to both force F and force G we should utilize

(a)  

Find the distance from the point S(1, 2, 1) to the line x=2-t, y=-1 +2t, z=2+2t

(a)  

Find the distance between the point S(1, 2, 1) to the line representing the path of a moving car given by x=2-t, y=-1 + 2t, z=2 + 2t

(a)  

Given a= 4i + 6j -5k and b= 2i -5j +3k , solve for a x b?

• 25i - 4j - 14k
• 33i - 4j + 14k
• 33i + 4j - 14k
• -7i -22j -32k

Many quantities in Geometry and Physics such as area, volume, temperature and time can be characterized by a single real number that is scaled to appropriate units of measure. These are called

• Vector quantities
• Matrix quantities
• Scalar quantities
• Complex quantities

Tags

CCSS.HSN.VM.A.1