angle between r=(i+j)+s(i+j+k) and r=(2i-j)+t( 2i+3j+k)

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\vec{r} = (2 \hat{i} + 3 \hat{j} + 9 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k})

\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 5 .

\to r = (1 \to i + 2 \to j + 3 \to k) + t (- 2 \to i + \to j + \to k)

\to r = (2 \to i + 3 \to j + 5 \to k) + s (\to i + 2 \to j + 3 \to k)

¯ ¯ ¯ r = (2 ¯ i - 3 ¯ j + ¯ ¯ ¯ k) + λ (¯ i + 4 ¯ j + 3 ¯ ¯ ¯ k)

¯ ¯ ¯ r = (¯ i - ¯ j + 2 ¯ ¯ ¯ k) + μ (¯ i + 2 ¯ j - 3 ¯ ¯ ¯ k)

\vec{r} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}) and \vec{r} = (2 \hat{i} - \hat{j} - \hat{k}) + μ (- \hat{i} + \hat{j} - \hat{k})

\vec{r} = (\hat{i} + \hat{j}) + λ (2 \hat{i} - \hat{j} + \hat{k}) and \vec{r} = (2 \hat{i} + \hat{j} - \hat{k}) + μ (4 \hat{i} - 2 \hat{j} + 2 \hat{k})

¯ ¯ ¯ r \times ¯ ¯ b = ¯ ¯ c \times ¯ ¯ b . ¯ ¯ ¯ r . ¯ ¯ ¯ a = 0, ¯ ¯ ¯ a = 2 ¯ i + 3 ¯ j - ¯ ¯ ¯ k, ¯ ¯ b = 3 ¯ i - ¯ j + ¯ ¯ ¯ k, ¯ ¯ c = ¯ i + ¯ j + 3 ¯ ¯ ¯ k

¯ ¯ ¯ r =

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