121302 A point on the plane determined by the points A \((1,1,-1), B(2,-1,0)\) and \(C(-1,0,2)\) among the following is

121303 The shortest distance between the lines
\(\overrightarrow{\mathbf{r}}=(4 \hat{\mathbf{i}}-\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}) \text { and }\)
\(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{2} \hat{\mathbf{k}})+\boldsymbol{\mu}(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}})\) is

121304 The equation of the plane passing through the line of intersection of planes
\(\pi_1=2 \mathrm{x}+6 \mathrm{y}+4 \mathrm{z}-7=0\)
\(\pi_1=x-y-2 z-2=0\) and perpendicular to the plane \(x+y+2 z-5=0\) is

121305 If the line passing through the points \((a, 2,-4)\) and \((5,3, b)\) crosses the \(\mathrm{ZX}\)-plane at the point \((-a+2 b, 0, a+b)\), then \(14 a+7 b\)

121302 A point on the plane determined by the points A \((1,1,-1), B(2,-1,0)\) and \(C(-1,0,2)\) among the following is

121303 The shortest distance between the lines
\(\overrightarrow{\mathbf{r}}=(4 \hat{\mathbf{i}}-\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}) \text { and }\)
\(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{2} \hat{\mathbf{k}})+\boldsymbol{\mu}(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}})\) is

121304 The equation of the plane passing through the line of intersection of planes
\(\pi_1=2 \mathrm{x}+6 \mathrm{y}+4 \mathrm{z}-7=0\)
\(\pi_1=x-y-2 z-2=0\) and perpendicular to the plane \(x+y+2 z-5=0\) is

121305 If the line passing through the points \((a, 2,-4)\) and \((5,3, b)\) crosses the \(\mathrm{ZX}\)-plane at the point \((-a+2 b, 0, a+b)\), then \(14 a+7 b\)

121302 A point on the plane determined by the points A \((1,1,-1), B(2,-1,0)\) and \(C(-1,0,2)\) among the following is

121303 The shortest distance between the lines
\(\overrightarrow{\mathbf{r}}=(4 \hat{\mathbf{i}}-\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}) \text { and }\)
\(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{2} \hat{\mathbf{k}})+\boldsymbol{\mu}(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}})\) is

121304 The equation of the plane passing through the line of intersection of planes
\(\pi_1=2 \mathrm{x}+6 \mathrm{y}+4 \mathrm{z}-7=0\)
\(\pi_1=x-y-2 z-2=0\) and perpendicular to the plane \(x+y+2 z-5=0\) is

121305 If the line passing through the points \((a, 2,-4)\) and \((5,3, b)\) crosses the \(\mathrm{ZX}\)-plane at the point \((-a+2 b, 0, a+b)\), then \(14 a+7 b\)

121302 A point on the plane determined by the points A \((1,1,-1), B(2,-1,0)\) and \(C(-1,0,2)\) among the following is

121303 The shortest distance between the lines
\(\overrightarrow{\mathbf{r}}=(4 \hat{\mathbf{i}}-\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}) \text { and }\)
\(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{2} \hat{\mathbf{k}})+\boldsymbol{\mu}(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}})\) is

121304 The equation of the plane passing through the line of intersection of planes
\(\pi_1=2 \mathrm{x}+6 \mathrm{y}+4 \mathrm{z}-7=0\)
\(\pi_1=x-y-2 z-2=0\) and perpendicular to the plane \(x+y+2 z-5=0\) is

121305 If the line passing through the points \((a, 2,-4)\) and \((5,3, b)\) crosses the \(\mathrm{ZX}\)-plane at the point \((-a+2 b, 0, a+b)\), then \(14 a+7 b\)