Let a- b-2-k- Then the point of intersection of the lines r-a-b-a- and r-b-a-b- is

The correct option is A 3î+ĵ k̂ We have a #160; = i + j b #160; = 2i k The point of intersection of line #160; r #160; ×a #160; ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a⃗=î+ĵ,...

Question

Let $\to a =^i +^j, \to b = 2^i -^k$ . Then the point of intersection of the lines $^r \times \to a = \to b \times \to a$ and $^r \times \to b = \to a \times \to b$ is

3^i +^j -^k

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3^i -^j -^k

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3^i - 3^j -^k

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3^i + 3^j +^k

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Solution

The correct option is A $3^i +^j -^k$
We have
$\to a = ˆ i + ˆ j$
$\to b = 2 ˆ i - ˆ k$
The point of intersection of line $\to r \times \to a = \to b \times \to a$
$(\to r - \to b) \times \to a = 0$
$\Rightarrow \to r - \to b = t \to a$
$\Rightarrow \to r = \to b + t \to a$
Again the points of intersection of line $\to r \times \to b = \to a \times \to b$
$(\to r - \to a) \times \to b = 0$
$\Rightarrow \to r - \to a = λ \to b$
$\Rightarrow \to r = \to a + λ \to b$

From the Both of line we get
$∴ λ = 1 t = 1$

The of the points of the intersection of the both given line
$\to r = \to a + \to b$
$= 3 ˆ i + ˆ j - ˆ k$
Hence, the option $A$ is the correct answer.

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Let →a=^i+^j, →b=2^i−^k. Then the point of intersection of the lines ^r×→a=→b×→a and ^r×→b=→a×→b is

Let $\to a =^i +^j, \to b = 2^i -^k$ . Then the point of intersection of the lines $^r \times \to a = \to b \times \to a$ and $^r \times \to b = \to a \times \to b$ is