Questions in vectors

Select	Question
	The position of a particle is given by $\overrightarrow r = (\overrightarrow i + 2\overrightarrow j - \overrightarrow k )$ momentum $\overrightarrow P = (3\overrightarrow i + 4\overrightarrow j - 2\overrightarrow k ).$The angular momentum is perpendicular to
	Two vector A and B have equal magnitudes. Then the vector A + B is perpendicular to
	Find the torque of a force $\overrightarrow F = - 3\hat i + \hat j + 5\hat k$ acting at the point $\overrightarrow r = 7\hat i + 3\hat j + \hat k$
	The value of $(\overrightarrow A + \overrightarrow B )\, \times (\overrightarrow A - \overrightarrow B )$ is
	If $\vec A$ and $\vec B$ are perpendicular vectors and vector $\vec A = 5\hat i + 7\hat j - 3\hat k$ and $\vec B = 2\hat i + 2\hat j - a\hat k.$ The value of a is
	A force vector applied on a mass is represented as $\vec F = 6\hat i - 8\hat j + 10\hat k$ and accelerates with $1\;m/{s^2}$. What will be the mass of the body in kg
	Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram
	The position vectors of radius are $2\hat i + \hat j + \hat k$ and $2\hat i - 3\hat j + \hat k$ while those of linear momentum are $2\hat i + 3\hat j - \hat k.$ Then the angular momentum is
	What is the value of linear velocity, if $\vec \omega = 3\hat i - 4\hat j + \hat k$ and $\vec r = 5\hat i - 6\hat j + 6\hat k$
	Dot product of two mutual perpendicular vector is