$A =2 \hat{ i }+\hat{ j }, B =3 \hat{ j }-\hat{ k }$ and $C =6 \hat{ i }-2 \hat{ k }$ Value of $A -2 B +3 C$ would be
$20 \hat{ i }+5 \hat{ j }+4 \hat{ k }$
$20 \hat{ i }-5 \hat{ j }-4 \hat{ k }$
$4 \hat{ i }+5 \hat{ i }+20 \hat{ k }$
$5 \hat{ i }+4 \hat{ j }+10 \hat{ k }$
If $P + Q = R$ and $| P |=| Q |=\sqrt{3}$ and $| R |=3$, then the angle between $P$ and $Q$ is
For what value of $x$, will the two vectors $A =2 \hat{ i }+2 \hat{ j }-x \hat{ k }$ and $B =2 \hat{ i }-\hat{ j }-3 \hat{ k }$ are perpendicular to each other?
A particle undergoes three successive displacements given by $s _1=\sqrt{2}\,m$ north-east, $s _2=2\,m$ due south and $s _3=4\,m , 30^{\circ}$ north of west, then magnitude of net displacement is
A boat is sent across a river with a velocity of $8\, km/hr$. If the resultant velocity of boat is $10 \,km/hr$, then velocity of the river is ........$km/hr$
The angles which the vector $A =3 \hat{ i }+6 \hat{ j }+2 \hat{ k }$ makes with the coordinate axes are