We were given a vector revision sheet.
I think it is out of 'smartstudy' guide.
Can someone please show me how to do these...was going really well at the start but now I have hit a wall.
Some I know but can't prove them.
1. The position vector of point P is given by
\tilde{i} + (1-2cos(\Theta))\tilde{j})
. OP is perpendicular to the line
if
A:
=\frac{1}{4})
B:
=\frac{1}{2})
C:
=\frac{1}{\sqrt{2}})
D:
=\frac{\pi}{4})
E:
=\frac{-1}{4})
--------------------------------------
2. The position vector
)
of a particle at time
)
is given by
=(2t-1)\tilde{i} + t^2\tilde{j})
. The Cartesian equation of the curve along which the particle moves is:
A:
^2, x\geqslant-1)
B:
^2, x\geqslant0)
C:
^2, x\geqslant1)
D:
^2, x\geqslant0)
C:
^2, x\geqslant-1)
-----------------------------------------
3. The position vector,
, of a particle at any time
is given by
=(h+acos(t))\tilde{i} + (k+bsin(t))\tilde{j}, \quad a,b,h,k \in R)
and
. The curve along which this particle moves is:
A: a straight line
B: a parabola
C: an ellipse
D: a circle
E: an hyperbola
------------------------------------------
4. OABC is a rhombus in which
and
.
Which one of the following could be used to prove that the diagonals of a rhombus are at right angles to each other?
A:
B:
.(\tilde{a}+\tilde{b})=0)
C:
.(\tilde{a}-\tilde{b})=0)
D:
.(\tilde{a}+\tilde{b})=\frac{\pi}{2})
E:
.(\tilde{a}-\tilde{b})=\frac{\pi}{2})
-----------------------------------------
5. A particle moves in the x-y plane so that its position vector
is given by
=acos(nt)\tilde{i} + asin(nt)\tilde{j})
.
Which one of the following is
incorrectA: the particle travels in a circular path.
B: the speed of the particle is not constant.
C: the particle starts its motion at (a,0).
D: the period of the motion is
.
E: the acceleration is always directed towards the origin.
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