Area of a rectangle having vertices A, B...

Area of a rectangle having vertices A, B, C and D with position vectors : `-hati + (1/2)hatj + 4hatk, hati + (1/2)hatj + 4hatk, hati - (1/2)hatj + 4hatk` and `-hati - (1/2)hatj + 4hatk`, respectively is:

A

`1/2`

B

1

C

2

D

4

Text Solution

Verified by Experts

Topper's Solved these Questions

VECTORS
MODERN PUBLICATION|Exercise Exercise|500 Videos
UNIT TEST-4
MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

Area of a rectangle having vertices : A(-hati+1/2 hatj+4hatk),B(hati+1/2hatj+4hatk),C(hati-1/2 hatj+4hatk),D(-hati-1/2hatj+4hatk) is :

Show that the four points A,B,C and D with position vectors 4hati+5hatj+hatk,-(hatj+hatk),(3hati+9hatj+4hatk) and 4(-hati+hatj+hatk) respectively are coplanar.

The point having position vectors 2hati+3hatj+4hatk,3hati+4hatj+2hatk and 4hati+2hatj+3hatk are the vertices of

A vectors which makes equal angles with the vectors 1/3(hati - 2hatj + 2 hatk ) , 1/5(-4hati - 3hatk) , hatj is:

Find 'lambda' so that the four points with position vectors -hati+3hatj+2hatk,3hati+lambda hatj+4hatk,5hati+7hatj+3hatk and -13hati+17hatj-hatk are coplanar.

Check whether the given three vectors are coplnar or non- coplanar : -2hati -2 hatj + 4hatk, -2hati + 4hatj -2hatk, 4hati - 2hatj - 2hatk .

Using scalar triple product, show that the four points given by position vectors hati+hatj+10hatk , 2hati+3hatj+11hatk , 3hati+2hatj+6hatk and hati-2hatj+4hatk are coplanar.

Show that the four points with position vectors 4hati+8hatj+12hatk,2hati+4hatj+6hatk,3hati+5hatj+4hatk and 5hati+8hatj+5hatk are coplanar.

MODERN PUBLICATION-VECTORS-Exercise

Determine the area of a parallelogram whose adjacent sides are represe...
Text Solution
|
Let the vectors veca and vecb be such that |veca| = 3 and |vecb| = sqr...
Text Solution
|
Area of a rectangle having vertices A, B, C and D with position vector...
Text Solution
|
Write down a unit vector in XY-plane, making an angle of 30^o with the...
Text Solution
|
Find the scalar components and magnitude of the vector joining the poi...
Text Solution
|
A girl walks 4 km towards west, then she walks 3 km in a direction 30^...
Text Solution
|
If veca = vecb + vecc, then is it true that |veca| = |vecb| + |vecc|?...
Text Solution
|
Find the value of x for which x(hati + hatj + hatk) is a unit vector.
Text Solution
|
Find a vector of magnitude 5 units, and parallel to the resultant of t...
Text Solution
|
If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatk,vecc=hati-2hatj+hatk, the...
Text Solution
|
Show that the points A(1,-2,-8), B(5,0,-2) and C(11,3,7) are collinear...
Text Solution
|
Find the position vector of a point R which divides the line joining t...
Text Solution
|
The two adjacent sides of a parallelogram are given by the vectors 2ha...
Text Solution
|
Show that the direction cosines of a vector equally inclined to the ax...
Text Solution
|
Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+4...
Text Solution
|
The scalar product of the vector hati+hatj+hatk with a unit vector alo...
Text Solution
|
If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...
Text Solution
|
Prove that (veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2, if and ...
Text Solution
|
If theta is the angle between two vectors veca and vecb, then veca c...
Text Solution
|
Let veca and vecb be two unit vectors and theta is the angle between t...
Text Solution
|