If the position vectors of the point A,B...

If the position vectors of the point `A,B,C` be `overset(^)i+overset(^)j,overset(^)i-overset(^)j and aoverset(^)i+boverset(^)j+coverset(^)k` respectively then the point `A,B,C` are collinear if

`a=b=c=1`

`a=1,b and c` are arbitary scalars

`a=b=c=0`

`c=0 ,a=1 and b` is arbitary scalar

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

VECTORS
TARGET PUBLICATION|Exercise Competitive Thinking|79 Videos
VECTORS
TARGET PUBLICATION|Exercise Evaluation Test|18 Videos
VECTORS
TARGET PUBLICATION|Exercise Evaluation Test|18 Videos
TRIGONOMETRIC FUNCTIONS
TARGET PUBLICATION|Exercise Evaluation Test|34 Videos

Similar Questions

Explore conceptually related problems

[overset(^)ioverset(^)koverset(^)j]+[overset(^)koverset(^)joverset(^)i]+[overset(^)joverset(^)koverset(^)i]

If the vectors 3overset(^)i+overset(^)j-5overset(^)k and aoverset(^)i+boverset(^)j-15overset(^)k are collinear, if

If three points A,B,C are collinear, whose position vectors are overset(^)i-2overset(^)j-8overset(^)k,5overset(^)i-2overset(^)k and 11overset(^)i+3overset(^)j+7overset(^)k respectively, then the ratio in which B divides AC is

If the vectors overset(^)i+2overset(^)k,overset(^)j+overset(^)k and lambda overset(^)i+mu overset(^)j collinear, then

If the vectors overset(^)i+3overset(^)j-2overset(^)k,2overset(^)i-overset(^)j+4k and 3overset(^)i+2overset(^)j+xoverset(^)k are coplanar, then the value of x is

If the vectors 3overset(^)i+2overset(^)j-overset(^)k and 6overset(^)i-4xoverset(^)j+yoverset(^)k are parallel, then the value of x and y will be

The points with position vectors 20overset(^)i+poverset(^)j,5overset(^)i-overset(^)j and 10overset(^)i-13overset(^)j are collinear. The value of p is

If the vectors -overset(^)i+3overset(^)j+2overset(^)k,-4overset(^)i+2overset(^)j-2overset(^)kand 5overset(^)i+lambdaoverset(^)j+muoverset(^)k are collinear then

If vectors overset(^)i+overset(^)j+overset(^)k,overset(^)j-overset(^)i,overset(^)i+2overset(^)j+aoverset(^)k are coplanar, then a is equal to

If the vectors 2overset(^)i-overset(^)j+overset(^)k,overset(^)i+2overset(^)j-3overset(^)k and 3overset(^)i+lambdaoverset(^)j+5overset(^)k be coplanar, then lambda=

TARGET PUBLICATION-VECTORS-Critical Thinking

If the vectors -overset(^)i+3overset(^)j+2overset(^)k,-4overset(^)i+2o...
Text Solution
|
If three points A,B and C have position vectors (1,x,3),(3,4,7) and (y...
Text Solution
|
If the position vectors of the point A,B,C be overset(^)i+overset(^)j,...
Text Solution
|
Three points whose position vectors are bara+barb,bara-barb and bara+k...
Text Solution
|
If bara,barb and barc be there non-zero vectors, no two of which are c...
Text Solution
|
If the points A,B,C and D have position vectors bara,2bara+barb,4bara+...
Text Solution
|
If bara=2barp+3barq-barr,barb=barp-2barq+2barr and barc=-2barp+barq-2b...
Text Solution
|
If bara+barb+barc=lambdabard and barb+barc+bard=mubara and bara,barb,b...
Text Solution
|
A and B are two points. The position vector of A is 6b-2a. A point P ...
Text Solution
|
If bar(a),bar(b),bar(c)are the position vectors of the points A, B, C ...
Text Solution
|
If bar(OA)=overset(^)i+3overset(^)j-2overset(^)k and bar(OB)=3overset(...
Text Solution
|
bara,barb are position vectors of points A and B. If P divides AB in t...
Text Solution
|
If 2bara+barb=3barc, then A divides BC in the ratio
Text Solution
|
In DeltaABC, P is the mid point of BC,Q divides CA internally in the r...
Text Solution
|
If overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + ...
Text Solution
|
If the points (1,1,2),(2,1,p),(1,0,3) and (2,2,0) are co-planar then ...
Text Solution
|
If the points A, B, C and D with position vectors overset(^)i+overset(...
Text Solution
|
If aoverset(^)i+overset(^)j+overset(^)k,overset(^)i-boverset(^)j+overs...
Text Solution
|
If the given vectors (-bc,b^2+bc,c^2+bc)(a^2+ac,-ac,c^2+ac) and (a^2+a...
Text Solution
|
If bara,barb,barc are non-zero, non collinear vectors, then the vector...
Text Solution
|