A pyramid with vertex at point P has a...

A pyramid with vertex at point `P` has a regular hexagonal base `A B C D E F` , Position vector of points A and B are `hat i and hat i + 2 hat j` The centre of base has the position vector ` hat i+ hat j+sqrt(3) hat kdot` Altitude drawn from `P` on the base meets the diagonal `A D` at point `Gdot` find the all possible position vectors of `Gdot` It is given that the volume of the pyramid is `6sqrt(3)` cubic units and `A P` is 5 units.

Topper's Solved these Questions

TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS
CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos
VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS
CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

Find the direction cosines of the vector hat i+2 hat j+3 hat kdot

If the position vectors of the points P and Q are 2hat(i)+hat(k) " and " -3hat(i)-4hat(j)-5hat(k) respectively, then vector vec(OP) is -

If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are collinear, then

The position vectors of the points A, B and C are -5hat(i)+hat(j), 5hat(i)+5hat(j) " and " 10hat(i)+7hat(j) , show that the points A, B, C are colinear.

Find the vector of magnitude 3, bisecting the angle between the vectors vec a=2 hat i+ hat j- hat k and vec b= hat i-2 hat j+ hat kdot

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

Find a vector magnitude 5 units, and parallel to the resultant of the vectors vec a=2 hat i+3 hat j- hat k and vec b= hat i-2 hat j+ hat kdot

A line passes through the point with position vector 2 hat i-3 hat j+4 hat k and is in the direction of 3 hat i+4 hat j-5 hat kdot Find the equations of the line in vector and Cartesian forms.

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

The position vectors of two given points P and Q are 8hat(i)+3hat(j) " and " 2hat(i)-5hat(j) respectively, find the magnitude and direction of the vector vec(PQ)

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions

If vec a , vec ba n d vec c are three non-zero non-coplanar vectors, ...
Text Solution
|
Let a, b, c be distinct non-negative numbers an the vectors ahati+aha...
Text Solution
|
A pyramid with vertex at point P has a regular hexagonal base A B C ...
Text Solution
|
ABCD is a parallelogram. If L and M be the middle points of BC and CD,...
Text Solution
|
A ,B ,C and D have position vectors vec a , vec b , vec c and vec d ,...
Text Solution
|
If vec aa n d vec b are two unit vectors and theta is the angle betwe...
Text Solution
|
A B C D is a quadrilateral. E is the point of intersection of th...
Text Solution
|
If vectors vec A B=-3 hat i+4 hat ka n d vec A C=5 hat i-2 hat j+4 ha...
Text Solution
|
A B C D parallelogram, and A1a n dB1 are the midpoints of sides B Ca n...
Text Solution
|
The position vectors of the points Pa n dQ with respect to the ori...
Text Solution
|
A point O is the centre of a circle circumscribed about a triangleA ...
Text Solution
|
If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec ...
Text Solution
|
Let A B C be triangle, the position vectors of whose vertices are re...
Text Solution
|
If | vec a+ vec b|<| vec a- vec b|, then the angle between vec aa...
Text Solution
|
' I ' is the incentre of triangle A B C whose corresponding sides are ...
Text Solution
|
Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB...
Text Solution
|
Locus of the point P, for which vec(OP) represents a vector with direc...
Text Solution
|
If vec xa n d vec y are two non-collinear vectors and A B C isa trian...
Text Solution
|
If hat i-3 hat j+5 hat k bisects the angle between hat a and - hat ...
Text Solution
|
If 4 hat i+7 hat j+8 hat k ,2 hat i+3 hat j+4hat ja n d2 hat i+5 hat j...
Text Solution
|