Exercise: Let u = [3, -2, 1], v = [1, 1, 1] and w = [2, -2,0]. The area of the parallelogram formed by u and v is A = √ The volume of the parallelepiped formed by u, v and w is = Given that the volume of a parallelepiped is the area of its base times its height, the height of the parallelepiped formed by u, v and w when its base is viewed as the parallelogram formed by u and v is h = * √ x. Check The parallelepiped formed by u and v and ku x V will have the same volume as the parallelepiped formed by u, v and w if k = t1/ x x .

Q: Q3) An open-top box is to be made by cutting small congruent squares from the corners of a…

A: Let the side of the square that is cut be x inch. After cutting the squares from the corners and…

Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Q: Let à = 6i+2j-5 k and b=mi +3j - 5k, If a x b = 5 i 10 j + 2 k, Find m: Find the area of the…

A:

Q: 3. Find the area of the rhombus. dl (2x +2) cm d2 (6x + 8) cm

A: As we know that the area for a rhombus when the p and q are the diagonal is:- A=pq2

Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, -1),…

A: The quadrilateral is formed by the vertices in the xy-plane defined by 0, 0, 1,-1, 3, 1, and 2, 8.…