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Question

Mathematics Question on Vector Algebra

If a→,b→\overrightarrow{a}, \overrightarrow{b} and c→\overrightarrow{c} are unit coplanar vectors, then the scalar triple product [2a→−b→2b→−c→2c→−a→][2\overrightarrow{a}-\overrightarrow{b}2\overrightarrow{b}-\overrightarrow{c}2\overrightarrow{c}-\overrightarrow{a}] is

A

0

B

1

C

−3-\sqrt{3}

D

3\sqrt{3}

Answer

0

Explanation

Solution

a→,b→,c→\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} are coplanar vectors, then 2a→−b→,2b→−c→and2c→−a→2\overrightarrow{a}-\overrightarrow{b}, 2\overrightarrow{b}-\overrightarrow{c} and 2\overrightarrow{c}-\overrightarrow{a} are also coplanar vectors
i.e.[2a→−b→      2b→−c→     2c→−a→]=0i.e. [2\overrightarrow{a}-\overrightarrow{b}\, \, \, \, \, \, 2\overrightarrow{b}-\overrightarrow{c}\, \, \, \, \, 2\overrightarrow{c}-\overrightarrow{a}]=0