Test for Collinearity of Vectors
Q. If a is any vector then (a×^i)2+(a×^j)2+(a×^k)2 =
Q. The area of the parallelogram whose diagonals are ^i−3^j+2^k, −^i+2^j is
Q. The value of b such that the scalar product of the vector ^i+^j+^k with the unit vector parallel to the sum of the vectors 2^i+4^j+5^k and b^i+2^j+3^k is one, is
Q. If the vectors →α=a^i+^j+^k, →β=^i+b^j+^k and →γ=^i+^j+c^k are coplanar where a≠1, b≠1, c≠1, then the value of 11−a+11−b+11−c equals
Q. Let →α=(λ−2)→a+→b and →β=(4λ−2)→a+3→b be two given vectors where vectors →a and →b are non-collinear. The value of λ for which vectors →α and →β are collinear, is:
Q. The points whose position vectors are 60i+3j, 40i−8j and ai−52j collinear, if
Q. Let →a, →b, →c are three unit vectors such that no two of the vectors are collinear. If the vector →a+→b is collinear with →c and the vector →b+→c is collinear with →a, then the value of |→a+→b+→c| is
Q. If a=2^i−^j−m^k and b=47^i−27^j+2^k are collinear, then the value of m is equal to
Q. Assertion :If three points P, Q and R have position vectors →a, →b and →c respectively, and 2→a+3→b−5→c=0, then the points P, Q and R must be collinear. Reason: If for three points A, B and C; −−→AB=λ−−→AC, then points A, B and C must be collinear.
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Both Assertion and Reason are incorrect
Q. If ¯a=^i+^j−2^k, ¯b=2^i−^j+^k and ¯c=3^i−^k then, find the scalars m and n such that ¯c=m¯a+n¯b.