If `veca,vecb,vecc` are linearly independent vectors, then which one of the following set of vectors is linearly dependent?

If veca,vecb and vecc are three vectors of which every pair is non colinear. If the vector veca+vecb and vecb+vecc are collinear with the vector vecc and veca respectively then which one of the following is correct? (A) veca+vecb+vecc is a nul vector (B) veca+vecb+vecc is a unit vector (C) veca+vecb+vecc is a vector of magnitude 2 units (D) veca+vecb+vecc is a vector of magnitude 3 units

If veca,vecb and vecc are three vectors of which every pair is non colinear. If the vector veca+vecb and vecb+vecc are collinear with the vector vecc and veca respectively then which one of the following is correct? (A) veca+vecb+vecc is a nul vector (B) veca+vecb+vecc is a unit vector (C) veca+vecb+vecc is a vector of magnitude 2 units (D) veca+vecb+vecc is a vector of magnitude 3 units

Statement-I : Two non zero, non collinear vectors are linearly independent. Statement-II : Any three coplanar vectors are linearly dependent. Which of the above statement is true?

If veca,vecb,vecc are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is (A) veca+vecb+vecc (B) veca/|veca|+vecb/|vecb|+vecc/|vecc| (C) veca/|veca|^2+vecb/|vecb|^2+vecc/|vecc|^2 (D) |veca|veca-|vecb|vecb+|vecc|vecc

If veca,vecb,vecc are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is (A) veca+vecb+vecc (B) veca/|veca|+vecb/|vecb|+vec/|vecc| (C) veca/|veca|^2+vecb/|vecb|^2+vecc/|vecc|^2 (D) |veca|veca-|vecb|vecb+|vecc|vecc

If veca,vecb,vecc are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is (A) veca+vecb+vecc (B) veca/|veca|+vecb/|vecb|+vec/|vecc| (C) veca/|veca|^2+vecb/|vecb|^2+vecc/|vecc|^2 (D) |veca|veca-|vecb|vecb+|vecc|vecc

Let veca, vecb, vecc be unit vectors such that veca + vecb + vecc = vec0. Which one of the following is correct ?