Question

Solve 4 and 5. Thanks.

Given: u- 31 + 4 u=-31+2)-5k 1. Some other vector wis drected in the xey plane 30 counterclockwise frorm the positive x axis, and has a magnitude of 11 units. Find the x and y components of w. 2. Find iu +D. IA 3. Find iu 4. Find the angle between iu and v. 5. Find ×

Answer 1

here,

u = 3 i + 4 j

v = - 3 i + 2 j - 5 k

4)

the magnitude of u , |u| = sqrt(3^2 + 4^2)

|u| = 5 units

the magnitude of v , |v| = sqrt(3^2 + 2^2 + 5^2)

|v| = 6.16 units

the angle between u and v , theta = arccos((u.v)/(|u|*|v|))

theta = arccos((3 * (-3) + 4 * 2)/(5 * 6.16))

theta = 91.86 degree

the angle between the vectors is 91.86 degree

5)

u X v = (3 i + 4 j) X ( - 3 i + 3 j - 5 k)

u X v = ( 3 * 3 k + 3 * 5 j + 4 * 3 k - 4 * 5 i)

u X v = ( - 20 i + 15 j + 21 k)