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Matrices

Question
CBSEENMA12035644
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Show that the four points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4)
are coplanar.

Solution

Given  four points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4).
therefore,
AB with rightwards arrow on top space equals space left parenthesis negative 4 i with hat on top minus 6 j with hat on top minus 2 k with hat on top right parenthesis AC with rightwards arrow on top space equals space left parenthesis negative i with hat on top plus 4 j with hat on top plus 3 k with hat on top right parenthesis AD with rightwards arrow on top space equals space left parenthesis negative 8 i with hat on top plus j with hat on top plus 3 k with hat on top right parenthesis therefore space space vertical line AB with rightwards arrow on top space space AC with rightwards arrow on top space space AD with rightwards arrow on top vertical line space equals space open vertical bar table row cell negative 4 end cell cell negative 6 end cell cell negative 2 end cell row cell negative 1 end cell 4 3 row cell negative 8 end cell 1 3 end table close vertical bar equals space minus 4 left parenthesis 12 space plus space 3 right parenthesis space plus space 6 left parenthesis negative 3 space plus space 24 right parenthesis space minus space 2 left parenthesis 1 space plus space 32 right parenthesis equals space minus 60 space plus space 126 space minus space 66 equals 0 Hence comma space Four space points space straight A comma space straight B comma space straight C comma straight D space are space coplanar.

Some More Questions From Matrices Chapter

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

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