Find the value of m for which the four points A(3,-2,-1), B(2,3,-4), C(-1,1,2) and D(4,5,m) are coplanar. 

Asked by Aswin | 5th Jan, 2016, 05:39: PM

Expert Answer:

AB with rightwards arrow on top equals left parenthesis 2 minus 3 comma space 3 plus 2 comma space minus 4 plus 1 right parenthesis space equals left parenthesis negative 1 comma space 5 comma space minus 3 right parenthesis AC with rightwards arrow on top equals left parenthesis negative 1 minus 3 comma space 1 plus 2 comma space 2 plus 1 right parenthesis space equals left parenthesis negative 4 comma space 3 comma space 3 right parenthesis AD with rightwards arrow on top equals left parenthesis 4 minus 3 comma space 5 plus 2 comma space straight m plus 1 right parenthesis space equals left parenthesis 1 comma space 7 comma space straight m plus 1 right parenthesis  Points space straight A comma space straight B comma space straight C comma space straight D space are space coplanner space if  open vertical bar table row cell negative 1 end cell 5 cell negative 3 end cell row cell negative 4 end cell 3 3 row 1 7 cell straight m plus 1 end cell end table close vertical bar equals 0 rightwards double arrow negative 1 left parenthesis 3 straight m plus 3 minus 21 right parenthesis minus 5 left parenthesis negative 4 straight m minus 4 minus 3 right parenthesis minus 3 left parenthesis negative 28 minus 3 right parenthesis equals 0 rightwards double arrow negative 3 straight m plus 18 plus 20 straight m plus 35 plus 93 equals 0 rightwards double arrow 17 straight m equals negative 146 rightwards double arrow straight m equals fraction numerator negative 146 over denominator 17 end fraction

Answered by Vijaykumar Wani | 6th Jan, 2016, 12:10: PM