Find the vector equation of the following from in scalar product from
$\to r = (^i +^j) + λ (^i -^j +^k) + μ (-^i + 2^j + 2^k)$

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Solution

$\to r = \to a + λ \to b + μ \to c This is equation of plane passing through \to a and parallel to \to b a n d \to c$
$\begin{matrix} \to r =^i +^j + λ (^i -^j +^k) + μ (-^i + 2^j + 2^k) a (x - 1) + b (y - 1) + c z = 0 N o r m a l v e c t o r o f p l a n e = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 1 - 1 & 2 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ =^i (- 4) -^j (3) +^k (1) = - 4^i - 3^j +^k Equation of plane - 4 (x - 1) - 3 (y - 1) + z = 0 - 4 x - 3 y + z + 7 = 0 4 x + 3 y - z - 7 = 0 \to r . (4^i + 3^j -^k) = 7 \end{matrix}$

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Similar questions

\to r =^i -^j + λ (^i +^j +^k) + μ (^i - 2^j + 3^k)

\to r = (^i + 2^j + 3^k) + λ (^i -^j +^k)

\to r = (2^i -^j -^k) + μ (-^i +^j -^k)

\to r =^i + 2^j +^k + λ (^i -^j +^k)

\to r = 2^i -^j -^k + μ (2^i +^j + 2^k)

\to r =^i -^j + λ (^i -^j +^k) + μ (^i - 2^j + 3^k)

\to r = (^i + 2^j +^k) + λ (^i -^j +^k)

\to r =^2 i -^j -^k + μ (^2 i +^j + 2^k)

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