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Mathematics Question on Vector Algebra

If four distinct points with position vectors a→,b→,c→\overrightarrow a,\overrightarrow b,\overrightarrow c and d→\overrightarrow d are coplanar, then [a→b→c→][\overrightarrow a \overrightarrow b \overrightarrow c] is equal to

A

[a→d→b→]+[d→c→a→]+[d→b→c→][\overrightarrow a \overrightarrow d \overrightarrow b]+[\overrightarrow d \overrightarrow c \overrightarrow a]+[\overrightarrow d\overrightarrow b\overrightarrow c]

B

[b→c→d→]+[d→a→c→]+[d→b→a→][\overrightarrow b \overrightarrow c \overrightarrow d]+[\overrightarrow d \overrightarrow a \overrightarrow c]+[\overrightarrow d\overrightarrow b\overrightarrow a]

C

[d→b→a→]+[a→c→c→]+[d→b→c→][\overrightarrow d \overrightarrow b \overrightarrow a]+[\overrightarrow a \overrightarrow c \overrightarrow c]+[\overrightarrow d\overrightarrow b\overrightarrow c]

D

[d→c→a→]+[b→d→a→]+[c→d→b→][\overrightarrow d \overrightarrow c \overrightarrow a]+[\overrightarrow b \overrightarrow d \overrightarrow a]+[\overrightarrow c\overrightarrow d\overrightarrow b]

Answer

[d→c→a→]+[b→d→a→]+[c→d→b→][\overrightarrow d \overrightarrow c \overrightarrow a]+[\overrightarrow b \overrightarrow d \overrightarrow a]+[\overrightarrow c\overrightarrow d\overrightarrow b]

Explanation

Solution

The Correct Option is (D):[d→c→a→]+[b→d→a→]+[c→d→b→][\overrightarrow d \overrightarrow c \overrightarrow a]+[\overrightarrow b \overrightarrow d \overrightarrow a]+[\overrightarrow c\overrightarrow d\overrightarrow b]