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Applications of Dot Product

If A × B = C ...

Question

If $\to A \times \to B = \to C + \to D$ , then select the correct alternative:

A

is parallel to

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B

is perpendicular to

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C

Component of = component of

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D

Component of = component of

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Solution

The correct option is D
Component of = component of

According to definition of cross-product $\to C + \to D$ is perpendicular to both $\to A$ and $\to B$

$i . e ., \to A . (\to C + \to D) = 0$

$o r \to A . \to C + \to A . \to D = 0$

or (component of $\to C$ along $\to A$ ) + (component of $\to D$ along $\to A$ )=0

or component of $\to C$ along $\to A = -$ component of $\to D$ along $\to A$

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Similar questions

If $\to A \times \to B = \to C + \to D$ , then select the correct alternative:

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

are non-coplanar vectors then the vector

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

is parallel to:

\to b, \to c, \to d

are non-coplanar vectors then the vector

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

\to b, \to c, \to d

are non-coplanar vectors, then the vector

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

\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

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