Show that the vectors and  are coplanar

Asked by Topperlearning User | 13th Aug, 2016, 07:01: PM

Expert Answer:

The vectors are coplanar, if  = 0

 a with rightwards arrow on top equals i minus 2 j plus 3 k comma space space b with rightwards arrow on top equals negative 2 i plus 3 j minus 4 k comma space space c with rightwards arrow on top equals i minus 3 j plus 5 k
b with rightwards arrow on top x c with rightwards arrow on top equals open vertical bar table row i j k row cell negative 2 end cell 3 cell negative 4 end cell row 1 cell negative 3 end cell 5 end table close vertical bar equals i left parenthesis 15 minus 12 right parenthesis minus j left parenthesis negative 10 plus 4 right parenthesis plus k left parenthesis 6 minus 3 right parenthesis
equals 3 i plus 6 j plus 3 k
a with rightwards arrow on top. left parenthesis b with rightwards arrow on top x c with rightwards arrow on top right parenthesis equals left parenthesis i minus 2 j plus 3 k right parenthesis. left parenthesis 3 i plus 6 j plus 3 k right parenthesis equals 3 minus 12 plus 9 equals 0
S o space a with rightwards arrow on top comma b with rightwards arrow on top comma c with rightwards arrow on top space a r e space c o p l a n a r

Answered by  | 13th Aug, 2016, 09:01: PM