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Definition of a Determinant

If a⃗,b⃗ ar...

Question

If $\to a, \to b$ are collinear, then which of the following is false?

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

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\to a \cdot \to b = a b

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\to a \times \to b = 0

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\to a \cdot \to b = 0

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Solution

The correct options are
B $\to a \times \to b = \to a$
C $\to a \cdot \to b = 0$
If $\to a$ and $\to b$ are collinear, we can write $\to b = λ \to a$ .

$\to a \times \to b = \to a \times λ \to a = λ \to a \times \to a = 0$
$\to a \cdot \to b = \to a \cdot λ \to a = λ \to a \cdot \to a = | \to a | | λ \to a | = | \to a | | \to b | = a b$

Hence, options $A$ and $D$ are false statements.

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Similar questions

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If →a,→b are collinear, then which of the following is false?

The correct options are B →a×→b=→a C →a⋅→b=0 If →a and →b are collinear, we can write →b=λ→a.→a×→b=→a×λ→a=λ→a×→a=0→a⋅→b=→a⋅λ→a=λ→a⋅→a=|→a||λ→a|=|→a||→b|=abHence, options A and D are false statements.

If $\to a, \to b$ are collinear, then which of the following is false?