The point of intersection of the lines r - a - b - a and r - b - a - b isA- a-b-B- a-C- bD- a - b

The correct option is D (a⃗+b⃗) r⃗×a⃗ = b⃗×a⃗ ⇒ (r⃗ b⃗)×a⃗=0⃗⇒r⃗ b⃗ = t a⃗ Also r⃗×b⃗ =a⃗×b⃗ ⇒ (b⃗+ta⃗)×b⃗ =a⃗×b⃗ ⇒b⃗×b⃗ + t a⃗×b⃗ = a⃗×b⃗ ⇒0⃗+ t a⃗×b⃗=a⃗× ...

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Byju's Answer

Standard IX

Mathematics

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

$\to a$

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$\to b$

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$(\to a + \to b)$

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$(\to a - \to b)$

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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

Q. Let

a = i + j

and

b = 2 i - k,

the point of intersection of the lines

r \times a = b \times a

and

r \times b = a \times b

Q. The point of intersection of the lines

\to r = \to a + s (\to b + \to c)

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\to a

and

\to b

are not parallel.

\to r = γ (\to b - \to a), \to r = 2 \to b + μ \to a

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are not parallel.

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The point of intersection of the lines →r×→a=→b×→a and →r×→b=→a×→b is

The correct option is C (→a+→b) →r×→a=→b×→a⇒(→r−→b)×→a=→0⇒→r−→b=t →aAlso →r×→b=→a×→b⇒(→b+t→a)×→b=→a×→b⇒→b×→b+t →a×→b=→a×→b⇒→0+t →a×→b=→a×→b⇒t →a×→b=→a×→b⇒t=1⇒→r=→a+→b

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