If the resultant of the vectors $\left( {\hat i + 2\hat j - \hat k} \right),\left( {\hat i - \hat j + 2\hat k} \right)$ and ${\rm{\vec C}}$ is a unit vector along the y-direction, then ${\rm{\vec C}}$ is

$\left( {{\rm{\vec P}} + {\rm{\vec Q}}} \right)$ is a unit vector along X-axis. If ${\rm{\vec P}} = \hat i - \hat j + \hat k,$ then what value is ${\rm{\vec Q}}?$

$\left( {{\rm{\vec P}} + {\rm{\vec Q}}} \right)$ is a unit vector along X-axis. If ${\rm{\vec P}} = \hat i - \hat j + \hat k,$ then what value is ${\rm{\vec Q}}?$

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes 3 and 4 units respectively, and their dot product is 6. What is the angle between them?

$\overrightarrow A \,.\,\overrightarrow B = - \left| A \right|\left| B \right|$, then

Find the vector component of vector $\overrightarrow A = 2\widehat i + 3\widehat j$ along the direction of $\overrightarrow B = \widehat i + \widehat j$

The dot product of two vectors A and B is zero. What is the angle between them?

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes A and B respectively. If $\vec{A} \cdot \vec{B} = -AB$, and neither A nor B is zero, which of the following is true about the angle $heta$ between the vectors?

A force is inclined at ${60^0}$ to the horizontal. If its rectangular component in the horizontal direction is 50 N, then magnitude of the force in the vertical direction is

If $\vec{A} = 2\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{B} = \hat{i} + 4\hat{j} - 2\hat{k}$, and $\vec{C}$ is a vector perpendicular to both $\vec{A}$ and $\vec{B}$ such that $\vec{C} \cdot (\hat{i} + \hat{j} - \hat{k}) = 3$, find the magnitude of $\vec{C}$.