Angle between Two Vectors
Trending Questions
Q. If the angle θ between the vectors a=2x2^i+4x^j+^k and b=7^i−2^j+x^k is such that 90∘ < θ < 180∘
then x lies in the interval:
then x lies in the interval:
- (0, 12)
- (12, 1)
- (1, 32)
- (12, 32)
Q. The points O, A, B, C, D are such that ¯¯¯¯¯¯¯¯OA=a, ¯¯¯¯¯¯¯¯OB=b, ¯¯¯¯¯¯¯¯OC=2a+3b and ¯¯¯¯¯¯¯¯¯OD=a−2b. If |a|=3|b|, then the angle between ¯¯¯¯¯¯¯¯¯BD , ¯¯¯¯¯¯¯¯AC is
- π3
- π4
- π6
- none of these
Q. Two adjacent sides of a parallelogram ABCD are given by ⟶AB=2^i+10^j+11^k and ⟶AD=−^i+2^j+2^k.
The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by
The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by
- 89
- √179
- 19
- 4√59
Q. If →a and →b are two vectors such that →a.→b=0 and →a×→b=→0, then
- →a||→b
- →a⊥→b
- either parallel or perpedicular
- None of the above
Q. The vectors →a=3^i−2^j+2^k and →b=−^i−2^k are the adjacent sides of a parallelogram.Then, angle between its diagonals is
- π4
- π3
- π2
- 2π3
Q. If →a and →b are two unit vectors inclined at an angle θ such that →a+→b is a unit vector, then θ is equal to
- π3
- π4
- π2
- 2π3
Q. If the vectors →a=(clog2x)^i−6^j+2^k and →b=(log2x)^i+2^j+3(clog2x)^k make an obtuse angle for any x∈(0, ∞) then c belongs to
- (−∞, 0)
- (−∞, −43)
- (−43, 0)
- (−43, ∞)
Q.
→a and →c are unit vectors and |→b|=4. The angle between →a and →c is cos−1(14).
If →b−2→c=λ→a, then λ is
3 or −4
14 or 34
−3 or 4
−14 or 34
Q. If a=−^i+^j+2^k, b=2^i−^j−^k then c=−2^i+^j+3^k, then the angle between 2a-c and a+b is:
- π4
- π3
- π2
- 3π4
Q. Let →a and →b be two vectors such that |→a|=1, |→b|=4 and →a⋅→b=2. If →c=(2→a×→b)−3→b, then the angle between →b and →c is
- π6
- π3
- 5π6
- 2π3
Q. If →a, →b are unit vectors such that the vector →a+3→b is perpendicular to 7→a−5→b and →a−4→b is perpendicular to 7→a−2→b, then the angle between →a and →b is
- π6
- π4
- π3
- π2
Q. If a=−^i+^j+2^k, b=2^i−^j−^k then c=−2^i+^j+3^k, then the angle between 2a-c and a+b is:
- π4
- π3
- π2
- 3π4
Q. If →a, →b, →c are three mutually perpendicular vectors of equal magnitude, then the angle θ which →a+→b+→c makes with any one of three given vectors is given by
- cos−1(1√3)
- cos−1(13)
- cos−1(2√3)
- None of these
Q. Two adjacent sides of a parallelogram ABCD are given by ⟶AB=2^i+10^j+11^k and ⟶AD=−^i+2^j+2^k.
The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by
The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by
- 89
- √179
- 19
- 4√59
Q. If →a, →b, →c are three mutually perpendicular vectors of equal magnitude, then the angle θ which →a+→b+→c makes with any one of three given vectors is given by
- cos−1(1√3)
- cos−1(13)
- cos−1(2√3)
- None of these
