Mathematics Vectors & 3D Geometry questions from JEE Main 2014.
Equation of the line of the shortest distance between the lines $\frac{ x }{ 1 } = \frac{ y }{ - 1 } = \frac{ z }{ 1 }$ and $\frac{ x - 1 }{ 0 } = \frac{ y + 1 }{ - 2 } = \frac{ z }{ 1 }$ is
If $\hat{x}, \hat{y}$ and $\hat{z}$ are three unit vectors in threedimensional space, then the minimum value of $|\hat{x}+\hat{y}|^2+|\hat{y}+\hat{z}|^2+|\hat{z}+\hat{x}|^2$
If $|\vec{c}|^2=60$ and $\vec{c} \times(\hat{i}+2 \hat{j}+5 \hat{k})=\overrightarrow{0}$, then a value of $\vec{c} \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})$ is: