12.4.23 Let u = 2j - 3k, v = 3i - 2j + 2k, w =

12.4.23 Let u = 2j - 3k, v = 3i - 2j + 2k, w = - 6i + 4j - 4k. Which vectors, if any are (a) perpendicular? (b) Parallel? (a) Which vectors are perpendicular? Select the correct choice below and fill in the answer box(es) within your choice. A. Vector is perpendicular to vectors . (Use a comma to separate answers as needed.) B. The vectors are perpendicular. (Use a comma to separate answers as needed.) C. None of the vectors are perpendicular.

Transcript

0:00 Hello everyone.

00:01 So in this question we have given u is equal to 2 j minus 3k, v is equal to 3i minus 2j plus 2k and w is equal to minus 6i plus 4j minus 4k.

00:12 Now we have to find which vectors are perpendicular vectors and which vectors are parallel vectors.

00:18 So now we will answer our question one by one.

00:21 So we know that if vector a multiplied by vector b, that is scalar multiplication of vector a and b is equal to 0 then we can say that a and b vector are perpendicular to each other.

00:43 So now we will find first scalar product of u and v.

00:49 So now the scalar product of u and v will be, u is 2j minus 3k and v is 3i minus 2 .000.

01:00 2 j plus 2k so on multiplication we will get 0 minus 4 minus 6 which is equal to minus 10 now we will find scalar product of v and w which is equal to v is equal to v is 3 i minus 2 j plus 2k multiplied by minus 6 i plus 4 j minus 4k so on we will get minus 18 minus 8 and minus 8 so minus 8 minus 8 minus 8 minus 16 minus 16 and minus 18 is equal to minus 34 so now similarly we will find the scalar product of u and w so which is equal to u is 2 j minus 3k and w is minus 6i plus 4j minus 4k.

02:06 So now which is equal to 0 then plus 8 and then plus 12.

02:12 And 8 plus 12 is equal to 20.

02:15 So as we can see here that scalar product of u and v is equal to minus 10 which is not equal to 0 then scalar product of u and w is equal to minus 34 which is not equal to 0 and a scalar product of u and w is equal to 20 which is not equal to 0.

02:36 So now we can say that therefore no vectors are perpendicular...

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