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Applications of Cross Product

If . and × ...

Question

If . and $\times$ represent dot product and cross product respectively then which of the following is meaningless?

A

(\to a \times \to b) . (\to c \times \to d)

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B

(\to a \times \to b) \times (\to c \times \to d)

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C

(\to a . \to b) . (\to c \times \to d)

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D

(\to a . \to b) \times (\to c \times \to d)

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Solution

The correct option is D $(\to a . \to b) \times (\to c \times \to d)$
Cross product can only occur for two vectors.
$a . b$ is just a scalar quantity.
Hence the option $D$ is meaningless.

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Similar questions

(\to b \times \to c) . (\to a \times \to d) + (\to c \times \to a) . (\to b \times \to d)

+ (\to a \times \to b) . (\to c \times \to d) =

\to a \times \to b = \to c \times \to d

\to a \times \to c = \to b \times \to d

\to a - \to d, \to b - \to c

\to a \times \to b = \to c \times \to d

\to a \times \to c = \to b \times \to d

, then the vectors

\to a - \to d

\to b - \to c

A

\to a \times \to b = \to c \times \to d

\to a \times \to c = \to b \times \to d

\to b - \to c

\to a - \to d

R

: If cross product of two non-zero vectors is zero vector then those two vectors are parallel

Q. The value of

(\to a \times \to b) . (\to c \times \to d) + (\to b \times \to c) . (\to a \times \to d) + (\to c \times \to a) . (\to b \times \to d)

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