WEBVTT 00:00:01.650 --> 00:00:19.160 If 𝐴𝐡𝐢𝐷 is a square with a side length of 81 centimeters and 𝐞 is a unit vector perpendicular to its plane, find the cross product of vector 𝚨𝚩 and vector πš©π‚. 00:00:20.370 --> 00:00:27.350 We are told that 𝐴𝐡𝐢𝐷 is a square with a side length of 81 centimeters. 00:00:28.130 --> 00:00:33.000 We are told that 𝐞 is a unit vector perpendicular to its plane. 00:00:33.670 --> 00:00:39.280 And we want to find the cross product of vectors 𝚨𝚩 and πš©π‚. 00:00:40.530 --> 00:01:05.390 The cross product of two vectors 𝚨 and 𝚩 is a vector perpendicular to the plane that contains 𝚨 and 𝚩 and whose magnitude is given by the magnitude of vector 𝚨 multiplied by the magnitude of vector 𝚩 multiplied by the magnitude of sin πœƒ, where πœƒ is the angle between the two vectors. 00:01:06.060 --> 00:01:15.220 Since each side of our square has length 81 centimeters, then the magnitude of vector 𝚨𝚩 is 81. 00:01:16.210 --> 00:01:20.430 Likewise, the magnitude of vector πš©π‚ is 81. 00:01:21.100 --> 00:01:27.470 Since the vectors are the sides of a square, the angle between them is 90 degrees. 00:01:28.310 --> 00:01:44.290 The cross product of vectors 𝚨𝚩 and πš©π‚ is therefore equal to 81 multiplied by 81 multiplied by the sin of 90 degrees multiplied by the unit vector 𝐞. 00:01:45.470 --> 00:01:49.350 We know that the sin of 90 degrees is equal to one. 00:01:50.070 --> 00:02:05.170 81 multiplied by 81 is 6,561, which means that the cross product of 𝚨𝚩 and πš©π‚ is 6,561𝐞.