Home
Class 12
MATHS
OABCDE is a regular hexagon of side 2 un...

OABCDE is a regular hexagon of side 2 units in the XY-plane in the first quadrant. O being the origin and OA taken along the x-axis. A point P is taken on a line parallel to the z-axis through the centre of the hexagon at a distance of 3 units from O in the positive Z direction. Then find vector `vec(AP)`.

A

`-hati+3hatj+sqrt(5)hatk`

B

`hati-sqrt(3)hatj+5hatk`

C

`-hati+sqrt(3)hatj+sqrt(5)hatk`

D

`hati+sqrt(3)hatj+sqrt(5)hatk`

Text Solution

Verified by Experts

The correct Answer is:
C
.
Here, coordinate of Q are `(2cos60^(@),2sin60^(@))`
`impliesQ(1,sqrt(3),0)`
`thereforeP(1,sqrt(3)z)`
`OP=3`
`implies sqrt(1+3+z^(2))=3` or `z^(2)=5`
`z=sqrt(5)`
`therefore P(1,sqrt(3),sqrt(5))implies OP=hati+sqrt(3)hatj+sqrt(5)hatk`
Now, `AP=OP-OA=hati+sqrt(3)hatj+sqrt(5)hatk-2hati`
`=-hati+sqrt(3)hatj+sqrt(5)hatk`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find equation of the line through the point(0, 2) making an angle (2pi)/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Find the equation of line intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.

Find the direction in which a straight line must be drawn through the point (-1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

Find the equation of the straight line intersecting y - axis at a distance of 2 units above the origin & making an angle 30^(@) with the positive direction of x-axis .

A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in figure . The wires carry currents of 10A each as shown. The segments L and M are along the x-axis. The segments P and Q are parallel to the y-axis such that OS = OR = 0.02m. Find magnitude and direction of the magnetic induction at the origin O.

The point (4, 1) undergoes the following transformations: (i) reflection about the line y = x (ii) translation through a distance of 2 units along the positive x-axis. Then the final co-ordinates of the point are :

A point (3,-2) undergoes the following transformations (i) reflection about the line y=x (ii) translation through a distance 3 units along -ve y -axis then the co-ordinates of final position of the point is

A line passes through the points whose position vectors are hati+hatj-2hatk and hati-3hatj+hatk . The position vector of a point on it at unit distance from the first point is

Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of x - axis is 15^(@) .