Consider points A,B,C annd D with positi...

Consider points A,B,C annd D with position vectors `7hati-4hatj+7hatk,hati-6hatj+10hatk,-1hati-3hatj+4hatk and 5hati-hatj+5hatk`, respectively. Then, ABCD is

square

rhombus

rectangle

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

VECTORS
VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|36 Videos
VECTORS
VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (INTEGER TYPE)|4 Videos
VECTORS
VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos
TRIGONOMETRIC IDENTITIES AND EQUATIONS
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

Consider points A, B, C and D with position vectors 7 hati - 4 hat j + 7 hat k , hati - 6 hat j + 10 hat k , - hati - 3 hatj + 4 hatk and 5 hati - hatj + 5 hatk respectively. Then, ABCD is a

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 values of a for which the points A, B, and C with position vectors 2hati - hatj + hatk, hati - 3hatj - 5hatk, and ahati - 3hatj + hatk ,respectively, are the vertices of a right-angled triangle with C = pi/2 are

Show that the points A,B and C having position vectors (3hati - 4hatj - 4hatk), (2hati - hatj + hatk) and (hati - 3hatj - 5hatk) respectively, from the vertices of a right-angled triangle.

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

The points with position vectors alpha hati+hatj+hatk, hati-hatj-hatk, hati+2hatj-hatk, hati+hatj+betahatk are coplanar if

If three points A, B and C have position vectors hati + x hatj + 3 hatk, 3 hati + 4 hatj + 7 hatk and y hati -2hatj - 5 hatk respectively are collinear, then (x, y) =

Show that the points A, B and C with position vectors -2hati+3hatj+5hatk, hati+2hatj+3hatk and 7hati-hatk respectively are collinear

The volume of the tetrahedron whose vertices are the points with positon vectors hati-6hatj+10hatk, -hati-3hatj+7hatk, 5hati-hatj+lambdahatk and 7hati-4hatj+7hatk is 11 cubic units if the value of lamda is

VMC MODULES ENGLISH-VECTORS -JEE MAIN (ARCHIVE)

Let veca,vecb and vecc be non-zero vectors such that no two are collin...
Text Solution
|
A tetrahedron has vertices O (0,0,0), A(1,2,1,), B(2,1,3) and C(-1,1,2...
Text Solution
|
If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^2)|=0 and vectors (1,a,a^2)...
Text Solution
|
If vecu,vecv and vecw are three non coplanar vectors then (vecu+vecv-v...
Text Solution
|
Consider points A,B,C annd D with position vectors 7hati-4hatj+7hatk,h...
Text Solution
|
Let A(3,0,-1), B(2,10,6) and C(1,2,1) be the vertices of a triangle an...
Text Solution
|
If a unit vector vec a makes angle pi//3 with hat i ,pi//4 with hat...
Text Solution
|
Let a=hati + hatj + sqrt(2)hatk, b=b(1)hati + b(2)hatj + sqrt(2)hatk a...
Text Solution
|
Prove that the line x=ay+b, z=cy+d and x=a'y+b', z=dy+d' are perpendic...
Text Solution
|
Let a=3hati + 2hatj + 2hatk and b= hati + 2hatj - 2hatk be two vectors...
Text Solution
|
Let alpha epsilon R and the three vectors veca=alpha hati+hatj+3hatk, ...
Text Solution
|
If the length of the perpendicular from the point (beta, 0,beta) (beta...
Text Solution
|
Let vecalpha = 3hati + hatj and beta= 2hati - hatj + 3hatk. If vecbeta...
Text Solution
|
Let a=3hati + 2hatj + xhatk and b = hati - hatj + hatk, for some real ...
Text Solution
|
The sum of the distinct real values of mu, for which the vectors, mu h...
Text Solution
|
If veca=hati+2hatj+4hatk, vecb=hati+lamdahatj+4hatk, vecc=2hati+4hatj+...
Text Solution
|
Let a=hati - hatj, b=hati + hatj + hatk and c be a vector such that a ...
Text Solution
|
Let a , b and c be three unit vectors out of which vectors b an...
Text Solution
|
Let alpha = (lambda-2) a + b and beta =(4lambda -2)a + 3b be two given...
Text Solution
|
Let veca = 2hati+lambda1 hatj+3hatk, vec(b)=4hati+(3-lambda2) hatj+6ha...
Text Solution
|