87695 If \(\alpha, \beta, \gamma\) are distinct real numbers are \(\alpha+\beta+\gamma\) \(\neq 0\), then the points with position vectors \(\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+\gamma \hat{k}, \beta \hat{\mathbf{i}}+\gamma \hat{j}+\alpha \hat{k}\) and \(\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}\) are

87696 If the points having the position vectors
\(3 \hat{i}-2 \hat{j}-\hat{k}, \hat{2} i+3 \hat{j}-4 \hat{k},-\hat{i}+\hat{j}+2 \hat{k} \text { and } 4 \hat{i}+5 \hat{j}+\lambda \hat{k}\)
are coplanar, then \(\lambda=\)

87697 If the position vectors of the points \(A, B, C, D\) are \(7 \hat{i}-4 \hat{j}+7 \hat{k}, \hat{i}-6 \hat{j}+10 \hat{k}\), \(-\hat{i}-3 \hat{j}+4 \hat{k}, 5 \hat{i}-\hat{j}+5 \hat{k}\) respectively, then \(A B C D\) is

87698 The distance of a point \((2,5,-3)\) from the plane \(6 x-3 y+2 z-4=0\) is

87695 If \(\alpha, \beta, \gamma\) are distinct real numbers are \(\alpha+\beta+\gamma\) \(\neq 0\), then the points with position vectors \(\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+\gamma \hat{k}, \beta \hat{\mathbf{i}}+\gamma \hat{j}+\alpha \hat{k}\) and \(\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}\) are

87696 If the points having the position vectors
\(3 \hat{i}-2 \hat{j}-\hat{k}, \hat{2} i+3 \hat{j}-4 \hat{k},-\hat{i}+\hat{j}+2 \hat{k} \text { and } 4 \hat{i}+5 \hat{j}+\lambda \hat{k}\)
are coplanar, then \(\lambda=\)

87697 If the position vectors of the points \(A, B, C, D\) are \(7 \hat{i}-4 \hat{j}+7 \hat{k}, \hat{i}-6 \hat{j}+10 \hat{k}\), \(-\hat{i}-3 \hat{j}+4 \hat{k}, 5 \hat{i}-\hat{j}+5 \hat{k}\) respectively, then \(A B C D\) is

87698 The distance of a point \((2,5,-3)\) from the plane \(6 x-3 y+2 z-4=0\) is

87695 If \(\alpha, \beta, \gamma\) are distinct real numbers are \(\alpha+\beta+\gamma\) \(\neq 0\), then the points with position vectors \(\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+\gamma \hat{k}, \beta \hat{\mathbf{i}}+\gamma \hat{j}+\alpha \hat{k}\) and \(\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}\) are

87696 If the points having the position vectors
\(3 \hat{i}-2 \hat{j}-\hat{k}, \hat{2} i+3 \hat{j}-4 \hat{k},-\hat{i}+\hat{j}+2 \hat{k} \text { and } 4 \hat{i}+5 \hat{j}+\lambda \hat{k}\)
are coplanar, then \(\lambda=\)

87697 If the position vectors of the points \(A, B, C, D\) are \(7 \hat{i}-4 \hat{j}+7 \hat{k}, \hat{i}-6 \hat{j}+10 \hat{k}\), \(-\hat{i}-3 \hat{j}+4 \hat{k}, 5 \hat{i}-\hat{j}+5 \hat{k}\) respectively, then \(A B C D\) is

87698 The distance of a point \((2,5,-3)\) from the plane \(6 x-3 y+2 z-4=0\) is

87695 If \(\alpha, \beta, \gamma\) are distinct real numbers are \(\alpha+\beta+\gamma\) \(\neq 0\), then the points with position vectors \(\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+\gamma \hat{k}, \beta \hat{\mathbf{i}}+\gamma \hat{j}+\alpha \hat{k}\) and \(\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}\) are

87696 If the points having the position vectors
\(3 \hat{i}-2 \hat{j}-\hat{k}, \hat{2} i+3 \hat{j}-4 \hat{k},-\hat{i}+\hat{j}+2 \hat{k} \text { and } 4 \hat{i}+5 \hat{j}+\lambda \hat{k}\)
are coplanar, then \(\lambda=\)

87697 If the position vectors of the points \(A, B, C, D\) are \(7 \hat{i}-4 \hat{j}+7 \hat{k}, \hat{i}-6 \hat{j}+10 \hat{k}\), \(-\hat{i}-3 \hat{j}+4 \hat{k}, 5 \hat{i}-\hat{j}+5 \hat{k}\) respectively, then \(A B C D\) is

87698 The distance of a point \((2,5,-3)\) from the plane \(6 x-3 y+2 z-4=0\) is