The value of p so that the vectors (2i-j+k),(i+2j-3k),(3i+pj+5k) are coplanar should be

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\vec{a} = \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k}, \vec{c} = λ \hat{i} - \hat{j} + λ \hat{k}

\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{c} = λ \hat{i} + λ \hat{j} + 5 \hat{k}

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{b} = 3 \hat{i} + λ \hat{j} + \hat{k}, \vec{c} = \hat{i} + 2 \hat{j} + 2 \hat{k}

\vec{a} = \hat{i} + 3 \hat{j}, \vec{b} = 5 \hat{k}, \vec{c} = λ \hat{i} - \hat{j}

a = 2 i - j + k, b = i + 2 j - 3 k, c = 3 i + λ j + 5 k

λ

i + 3 j - 2 k, 2 i - j + 4 k

3 i + 2 j + p k

3 \hat{i} + \hat{j} - \hat{k}, 2 \hat{i} - \hat{j} + 7 \hat{k} and 7 \hat{i} - \hat{j} + 23 \hat{k}

\hat{i} + 2 \hat{j} + 3 \hat{k}, 2 \hat{i} + \hat{j} + 3 \hat{k} and \hat{i} + \hat{j} + \hat{k}

2 ˆ i + 3 ˆ j - 2 ˆ k, 5 ˆ i + n ˆ j + ˆ k and - ˆ i + 2 ˆ j + 3 ˆ k

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