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 .........$N$
$15$
$3$
$17$
$2$
Given $a+b+c+d=0,$ which of the following statements eare correct:
$(a)\;a, b,$ c, and $d$ must each be a null vector,
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$
$(c)$ The magnitude of a can never be greater than the sum of the magnitudes of $b , c ,$ and $d$
$(d)$ $b + c$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear, and in the line of a and $d ,$ if they are collinear ?
Establish the following vector inequalities geometrically or otherwise:
$(a)$ $\quad| a + b | \leq| a |+| b |$
$(b)$ $\quad| a + b | \geq| a |-| b |$
$(c)$ $\quad| a - b | \leq| a |+| b |$
$(d)$ $\quad| a - b | \geq| a |-| b |$
When does the equality sign above apply?
Three girls skating on a circular ice ground of radius $200 \;m$ start from a point $P$ on the edge of the ground and reach a point $Q$ diametrically opposite to $P$ following different paths as shown in Figure. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?
When vector $\overrightarrow{ A }=2 \hat{ i }+3 \hat{ j }+2 \hat{ k }$ is subtracted from vector $\vec{B}$, it gives a vector equal to $2 \hat{j}$. Then the magnitude of vector $\vec{B}$ will be: