Consider a square pyramid with its base sitting on the x-y plane and the apex on the z-axis. The base is defined by four points: (1,0,0), (0,1,0),(-1,0,0), (0,-1,0). The apex is at (0,0,2). Use vector cross product to find the unit normal vector for each triangular face of the pyramid. This is similar to problem G1.4.
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- Consider the force vector F=<1,1,1/2>. If the magnitude of the torque T=OP*F is equal to the area of the equilateral triangle formed by the origin, P, and (1,-1,1), then determine the acute angle formed by OP and F. Give your answer in degrees.Using the definition of dot product: A B = ABCOS (0AB) = AxBx + Ay By + A₂B₂ Find the angle between the following vectors: (c) A = 1î + 3j+0k B = 3î + 1) + Ok A = 1î - 3j + 2k B = -31 + 1) + 0k (b) (d) A = 1î + 1ĵ + Ok B = 21-3j+0k A = 21-5j-1k B = 3î + 11 + 3kVector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise from the positive x axis, whereas the vector B has a magnitude of 3m and lies in the yz plane directed at 30 degrees from the positive z axic. Find the cross product A x B and the angle between the vectors.
- A vector a of magnitude 17 units and another vector b of magnitude 8.5 units differ in directions by 72°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product a×b.Given the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following. (a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.) ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.) ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.) °Find a unit vector perpendicular to A = (î+ ĵ – Îk) and B = ( 2i + j- 3k). (Hints. One method to find the unit vector C perpendicular to A and B will be to use the fact that the cross product is perpendicular to both vectors A and B, but keep in mind that the magnitude of the unit vector is one. There is another method which is a little bit longer by using the fact that the dot product AC=0 and BC=0 where C is the unit vector )