**Question 1.** Find **i × j** and **i · (j × k)**. Give a geometric interpretation of both quantities.**Explanation:**1. **i × j:** - The cross product **i × j** results in vector **k**. This is because **i**, **j**, and **k** are unit vectors along the x, y, and z axes, respectively, in a right-handed coordinate system. The cross product of any two unit vectors in this system results in the third.2. **i · (j × k):** - The expression **j × k** results in vector **i** (based on the cyclic nature of unit vectors in a right-handed coordinate system). - The dot product **i · i** equals 1 because the dot product of a vector with itself equals the square of its magnitude, and a unit vector has a magnitude of 1.**Geometric Interpretation:**- **i × j = k** implies that the cross product of two perpendicular vectors in a plane gives a vector perpendicular to that plane (along the z-axis in this context).- **i · (j × k) = 1** indicates that the volume of the parallelepiped formed by vectors **i**, **j**, and **k** is 1, which geometrically represents the scalar triple product and confirms the orthogonality and unit length of these vectors.

Name: **Question 1.** Find **i × j** and **i · (j × k)**. Give a geometric
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Question 1.** Find **i × j** and **i · (j × k)**. Give a geometric interpretation of both quantities.**Explanation:**1. **i × j:** - The cross product **i × j** results in vector **k**. This is because **i**, **j**, and **k** are unit vectors al