Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$

Give the names of two methods for vector addition. Write the law of parallogram for vector addition.

The magnitudes of vectors $\vec A,\,\vec B$ and $\vec C$ are $3, 4$ and $5$ units respectively. If $\vec A + \vec B = \vec C$, the angle between $\vec A$ and $\vec B$ is

If $|{\overrightarrow V _1} + {\overrightarrow V _2}|\, = \,|{\overrightarrow V _1} - {\overrightarrow V _2}|$ and ${V_2}$ is finite, then

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The direction of the forces are unknown. The resultant force on the body may be .........$N$

A cyclist starts from the centre $O$ of a circular park of radius $1\; km$, reaches the edge $P$ of the park, then cycles along the circumference, and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$, what is the

$(a)$ net displacement,

$(b)$ average velocity, and

$(c)$ average speed of the cyclist ?