# Vector Operations

Vector operations are fundamental mathematical processes that play a pivotal role in various fields, including physics, engineering, and computer science. These operations involve manipulating vectors, which are quantities characterized by magnitude and direction. By performing operations such as addition, subtraction, scalar multiplication, and dot product, vectors can be combined, transformed, and analyzed to solve complex problems and model real-world phenomena. Understanding vector operations is essential for mastering advanced concepts in areas such as linear algebra, mechanics, and computer graphics, making them indispensable tools for researchers, engineers, and practitioners alike.

- What is the cross product of #[3,2, 5]# and #[1,2,-4] #?
- How do you normalize # (2i + 3j – 7k) #?
- A farmer wants to wall off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, where A = 4.99 km, B = 2.46 km, and C = 3.23 km and then correctly calculates the length and orientation of D?
- What is the angle between two forces of equal magnitude, #F_a# and #F_b#, when the magnitude of their resultant is also equal to the magnitude of either of these forces?
- What is the cross product of #[2, 1, -4]# and #[4,3,6] #?
- What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # (4 i + 4 j + 2 k) #?
- What is the unit vector that is orthogonal to the plane containing # (2i + 3j – 7k) # and # (3i + 2j - 6k) #?
- What is the projection of #(3i + 2j - 6k)# onto # (3i - j - 2k)#?
- What is #|| <-8, 3, -1> - < 4 , -5, 3 > ||#?
- What is the cross product of #[1, 4, -2]# and #[3, 0, 5] #?
- What is #|| <7, 3, -1> - < -2 , 5, 3 > ||#?
- What is the unit vector that is orthogonal to the plane containing # (20j +31k) # and # (32i-38j-12k) #?
- How do you normalize #(- 4i + 5 j- k)#?
- What is the cross product of #<2 , 5 ,-7 ># and #<5 ,6 ,-9 >#?
- What is the cross product of #[2,-1,2]# and #[1,-1,3] #?
- What is #|| <4, 9, 7 > - < 9, -1, 2> ||#?
- What is the unit vector that is normal to the plane containing #( i +k )# and #(2i+ j - 3k)?
- How can I calculate the magnitude of vectors?
- What is the unit vector that is orthogonal to the plane containing # (8i + 12j + 14k) # and # (3i – 4j + 4k) #?
- What is the cross product of #[1, -2, -3]# and #[1, 3, 4]#?