87818
The work done by the force \(4 \hat{i}-3 \hat{j}+2 \hat{k}\) in moving a particle along a straight line from the point \((3,2,-1)\) to \((2,-1,4)\) is
87819
A parallelogram is constructed on the vectors \(\vec{a}=3 \alpha-\beta, \vec{b}=\alpha+3 \beta\). If \(|\alpha|=|\beta|=2\) and the angle between \(\alpha\) and \(\beta\) is \(\frac{\pi}{3}\), then length of a diagonal of the parallelogram is
87728
If \(a, b, c\) are non- negative distinct numbers and \(\quad \hat{i}+\hat{\mathbf{j}}+\mathbf{c} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{b} \hat{\mathbf{k}}\) are coplanar vectors, then
87727
If \(\overrightarrow{\mathbf{a}}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is the root of the equation
87818
The work done by the force \(4 \hat{i}-3 \hat{j}+2 \hat{k}\) in moving a particle along a straight line from the point \((3,2,-1)\) to \((2,-1,4)\) is
87819
A parallelogram is constructed on the vectors \(\vec{a}=3 \alpha-\beta, \vec{b}=\alpha+3 \beta\). If \(|\alpha|=|\beta|=2\) and the angle between \(\alpha\) and \(\beta\) is \(\frac{\pi}{3}\), then length of a diagonal of the parallelogram is
87728
If \(a, b, c\) are non- negative distinct numbers and \(\quad \hat{i}+\hat{\mathbf{j}}+\mathbf{c} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{b} \hat{\mathbf{k}}\) are coplanar vectors, then
87727
If \(\overrightarrow{\mathbf{a}}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is the root of the equation
87818
The work done by the force \(4 \hat{i}-3 \hat{j}+2 \hat{k}\) in moving a particle along a straight line from the point \((3,2,-1)\) to \((2,-1,4)\) is
87819
A parallelogram is constructed on the vectors \(\vec{a}=3 \alpha-\beta, \vec{b}=\alpha+3 \beta\). If \(|\alpha|=|\beta|=2\) and the angle between \(\alpha\) and \(\beta\) is \(\frac{\pi}{3}\), then length of a diagonal of the parallelogram is
87728
If \(a, b, c\) are non- negative distinct numbers and \(\quad \hat{i}+\hat{\mathbf{j}}+\mathbf{c} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{b} \hat{\mathbf{k}}\) are coplanar vectors, then
87727
If \(\overrightarrow{\mathbf{a}}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is the root of the equation
87818
The work done by the force \(4 \hat{i}-3 \hat{j}+2 \hat{k}\) in moving a particle along a straight line from the point \((3,2,-1)\) to \((2,-1,4)\) is
87819
A parallelogram is constructed on the vectors \(\vec{a}=3 \alpha-\beta, \vec{b}=\alpha+3 \beta\). If \(|\alpha|=|\beta|=2\) and the angle between \(\alpha\) and \(\beta\) is \(\frac{\pi}{3}\), then length of a diagonal of the parallelogram is
87728
If \(a, b, c\) are non- negative distinct numbers and \(\quad \hat{i}+\hat{\mathbf{j}}+\mathbf{c} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{b} \hat{\mathbf{k}}\) are coplanar vectors, then
87727
If \(\overrightarrow{\mathbf{a}}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is the root of the equation
87818
The work done by the force \(4 \hat{i}-3 \hat{j}+2 \hat{k}\) in moving a particle along a straight line from the point \((3,2,-1)\) to \((2,-1,4)\) is
87819
A parallelogram is constructed on the vectors \(\vec{a}=3 \alpha-\beta, \vec{b}=\alpha+3 \beta\). If \(|\alpha|=|\beta|=2\) and the angle between \(\alpha\) and \(\beta\) is \(\frac{\pi}{3}\), then length of a diagonal of the parallelogram is
87728
If \(a, b, c\) are non- negative distinct numbers and \(\quad \hat{i}+\hat{\mathbf{j}}+\mathbf{c} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{b} \hat{\mathbf{k}}\) are coplanar vectors, then
87727
If \(\overrightarrow{\mathbf{a}}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is the root of the equation
