Equal Vectors
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Q. Let →a=^i+^j+^k, →b and →c=^j−^k be three vectors such that →a×→b=→c and →a⋅→b=1. If the length of projection vector of the vector→b on the vector →a×→c is l, then the value of 3l2 is equal to
Q. If the vector b = 3j + 4k is written as the sum of a vector b_1 parallel to a = i + j and a vector b_2 perpendicular to a , thenb_{1 }× b_2 is equal to:
Q. Which of the following is/are true?
1) Equal vectors have same direction but not necessarily the same magnitude.
2) Equal vectors have same magnitude and same direction.
3) Equal vectors cannot start from different points.
1) Equal vectors have same direction but not necessarily the same magnitude.
2) Equal vectors have same magnitude and same direction.
3) Equal vectors cannot start from different points.
- 1, 2 and 3 are true
- Only 2 is true
- None of them is true
- 2 and 3 are true
Q. 11. If a b and c are mutually perpendicular vectors of equal magnitude find angles which the vector 2a + b + 2c makes with the vectors a , b and c
Q. If →a, →b, →c are non coplanar vectors and λ is a real number, then the vectors →a+2→b+3→c, λ→b+4→c and (2λ−1)→c are non coplanar for:
- all values of λ
- all except one values of λ
- all except two values of λ
- no values of λ
Q. If 0.4i + 0.8j + bk is a unit vector . What is the value of b?
Q.
Find the value of n so that may be the geometric mean between a and b.