Find the point of intersection of the lines r-1-1-1-k3-1-0-k - R and r-4-0-1-k2-0-3-K - R-

Solution r⃗ = (1, 1, 1)+k(3, 1, 0) r⃗ = (4, 0, 1) + k (2, 0,3 ) Assuming point r line (1) ( 3 λ #160; +1, λ +1, 1 ) putting in line (2) equat ...

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Family of Straight Lines

Find the poin...

Question

Find the point of intersection of the lines $\to r = (1, 1, - 1) + k (3, - 1, 0), k ϵ R$ and $\to r = (4, 0, 1) + k (2, 0, 3), K ϵ R$ .

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

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

\to r = (^i +^j -^k) + λ (3^i -^j)

\to r = (4^i -^k) + μ (2^i + 3^k)

\to r \cdot (3 \to i - \to j + \to k) = 1

\to r \cdot (3 \to i + 4 \to j - 2 \to k) = 2

\to r = (^i +^j +^k) + λ (3^i -^j)

\to r = (4^i -^k) + μ (2^i + 3^j)

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