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Cross Product of Two Vectors

The point of ...

Question

The point of intersection of the lines $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$ is

A

$\to a$

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B

$\to b$

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C

$(\to a + \to b)$

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D

$(\to a - \to b)$

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Solution

The correct option is C
$(\to a + \to b)$

$\to r \times \to a = \to b \times \to a \Rightarrow (\to r - \to b) \times \to a = \to 0 \Rightarrow \to r - \to b = t \to a A l s o \to r \times \to b = \to a \times \to b \Rightarrow (\to b + t \to a) \times \to b = \to a \times \to b \Rightarrow \to b \times \to b + t \to a \times \to b = \to a \times \to b \Rightarrow \to 0 + t \to a \times \to b = \to a \times \to b \Rightarrow t \to a \times \to b = \to a \times \to b \Rightarrow t = 1 \Rightarrow \to r = \to a + \to b$

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Similar questions

The point of intersection of the lines $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$ is

\to a = ˆ i + ˆ j

\to b = 2 ˆ i - ˆ k

, then the point of intersection of lines

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

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

\to a =^i +^j

\to b = 2^i +^j

The point of intersection of the lines

\to r \times \to a = \to b \times \to a & \to r \times \to b = \to a \times \to b

\to a =^i +^j

\to b = 2^i -^k

. The point of intersection of the lines

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

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

\to a = 3^i + 2^j, \to b = 2^i -^k,

then the point of intersection of the lines

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

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

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