If the vectors `ahati+bhatj+chatk,bhati+chatj+ahatk and chati+ahatj+bhatk` are coplanar and a,b,c are distinct then (A) `a^3+b^3+c^3=1` (B) `a+b+c=1` (C) `1/a+1/b+1/c=1` (D) a+b+c=0`

If the vectors 2ahati+bhatj+chatk, bhati+chatj+2ahatk and chati+2ahatj+bhatk are coplanar vectors, then the straight lines ax+by+c=0 will always pass through the point

If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1, b!=1,c!=1) are coplanar then the value of 1/(1-a)+1/(1-b)+1/(1-c) is (A) 0 (B) 1 (C) -1 (D) 2

Let a, b and c be distinct non-negative numbers. If vectos a hati +a hatj +chatk, hati + hatk and chati +chatj+bhatk are coplanar, then c is

Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj+chatk, hati+hatk and chati+chatj+bhatk lies in a plane then c is

If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, vecc=hati+chatj+c^(2)hatk are three non-coplanar vectors and |(a, a^(2), 1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0 , then the value of abc is

If a/b+b/a=1, then a^3+b^3=? (a) 1 (b) -1 (c) 1/2 (d) 0

If the position vectors of the points A,B and C be hati+hatj,hati-hatj and ahati+bhatj+chatk respectively, then the points A,B and C are collinear, if

Find the condition that the three points whose position vectors, a=ahati+bhatj+chatk,b=hati+chatj and c=-hati-hatj are collinear.

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to