Analysis 1

1. Cross product Using the right-hand rule, label the other two axes in the coordinate system. Sketch the following vectors, on a 3D view, to see where they are located. a a-I0 -1 3] in. b [0-2 0] in. 2= [2 3 in. Show your work to compute, by hand, ax b. Sketch also vector d above. Use "norm" and "cross" commands in MATLAB to calculate the magnitude of vector d: Yes Is the magnitude of a x b equal to the area of the parallelogram formed by vectors a and b? No Indicate that area by shading the right area above. Use the "cross" command in MATLAB, e.g. cross(b, a), to compute: axc Group C: 17:45-19:00 Page 1 of 4 Thursday, Feb 19 2. Scalar Triple Product The (scalar) triple product is defined as the dot product of one of the vectors with the cross product of the other two, i.e.: a (bxc) Absolute value of the triple product is the volume of the parallelepiped formed by the 3 vectors. Using the right-hand rule, label the other two axes in the coordinate system above. Sketch the following vectors, on a 3D view, to see where they are located. a-a [6 0 0] in. in. Form a parallelepiped with these 3 vectors; make sure it looks like a box. Find a (bx c) by hand; notice well that the result is a scalar quantity. a.(bxc)- Using MATLAB, find the determinant of the matrix that computes: c (ax b)- Spring UTRGV Mech. Eng. Department Show below your calculations to find the volume of the parallelepiped; Vol- base area x height: Is the absolute value of the triple product equal to the volume of the parallelepiped formed by the three vectors? Yes No 3. Dot Product Using the right-hand rule, label the other two axes in the coordinate system above. Sketch the following vectors, on a 3D view. or a 13 0 6] meters h-b=[-2 4 5] meters c- 17 2 0] meters Show your work by hand to compute a c: a c Find the unit vector for each vectors a and . Call them ua and uc. The final results must be in decimal with at least 3 digits after dot