Let r- - a- - -l- and r- - b- - -m- be two lines in space where a- - 5 - - - - 2 k- b- - - - 7 - - 8 k- l- - -4 - - - - k- and m- - 2 - - 5 - - 7 k- then the p-v- of a point which lies on both of these lines- is

The correct option is A î + 2 ĵ + k̂ r⃗_⃗1⃗ = a⃗+λî r⃗_⃗1⃗ = (5î+ĵ+2k̂)+λ ( 4î+ĵ k̂) r⃗_⃗1⃗ = (5 4λ )î+(1+λ )ĵ+(2 λ )k̂ #160; r⃗_⃗2⃗ = ...

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Applications of Dot Product

Let r⃗ = a⃗...

Question

Let $\to r = \to a + λ \to l$ and $\to r = \to b = μ \to m$ be two lines in space where $\to a = 5^i +^j + 2^k, \to b =^i + 7^j + 8^k, \to l = - 4^i +^j -^k a n d \to m = 2^i - 5^j - 7^k$ then the p.v. of a point which lies on both of these lines, is

^i + 2^j +^k

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2^i +^j +^k

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^i +^j + 2^k

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non existent as the lines are skew

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Solution

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Similar questions

\to r = \to a + λ \to l

\to r = \to b + μ \to m

\to a = 5^i +^j + 2^k

\to b = -^i + 7^j + 8^k

\to l = 4^i +^j -^k] a n d \to m = 2^i - 5^j - 7^(k

\to r = \to a + λ \to l

\to r = \to b + μ \to m

\to a = 5^i +^j + 2^k,

\to b = -^i + 7^j + 8^k,

\to l = - 4^i + 7^j -^k

\to m = - 2^i - 5^j - 7^k

\to a =^i +^j

\to b = 2^i -^k

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

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

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

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

\to r = l \to a + m \to b + n \to c

\to a =^i +^j

\to b = 2^i +^j

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

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