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Multiplication with Vectors

If A × B = C,...

Question

If $\to A \times \to B = \to C$ , then choose the incorrect option.

A

\to C ⊥ (\to A + \to B)

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B

\to C ⊥ (\to A - \to B)

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C

\to C ⊥ (\to A \times \to B)

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D

\to C ⊥ \to A

and

\to B

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Solution

The correct option is C $\to C ⊥ (\to A \times \to B)$
Given:
$\to A \times \to B = \to C$
So, $\to A \times \to B$ and $\to C$ are the same vectors.
Thus, $\to C ∥ (\to A \times \to B)$ .
Therefore, $(c)$ is the incorrect option.

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Similar questions

\to A \times \to B = \to C,

then which of the following statement is wrong?

\to a, \to b, \to c

are three non-zero vectors such that

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

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

, then choose the incorrect option(s)

Q. The length of the perpendicular from the origin to the plane passing through three non-collinear points

\to a, \to b, \to c

If $\to a \times \to b = \to c, \to b \times \to c = \to a$ and a,b,c be the moduli of the vectors $\to a, \to b, \to c$ respectively, then

\to a =^i +^j +^k

\to b = - 3^i +^k

\to c =^i + 2^j + 3^k

, then the ascending order of magnitudes of

A)

[\to a \times \to b

\to b \times \to c

\to c \times \to a]

B)

[\to a + \to b

\to b + \to c

\to c + \to a]

C)

[\to a

\to b

\to c]

[\to a

\to b

\to c]^{- 1}

D)

[\to a - \to b

\to b - \to c

\to c - \to a]

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Multiplication with Vectors

Standard XII Physics

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