Unit Vectors
Trending Questions
Q.
The unit vector along is:
Q. If a unit vector →a makes an angle π3 with ^i, π4 with ^j and θ∈(0, π) with ^k, then a value of θ is :
- 5π12
- π4
- 2π3
- 5π12
Q.
If the angle between two vectors A and B is , then its resultant C will be
Q. If →a and →b are unit vectors, then what is the angle between →a and →b for √3 →a−→b to be unit vector?
- 30∘
- 90∘
- 60∘
- 45∘
Q. Let ^a and ^b be two unit vectors such that the angle between them is π4. If θ is the angle between the vectors ^a+^b and (^a+2^b+2(^a×^b)), then the value of 164cos2θ is equal to :
- 45+18√2
- 90+27√2
- 54+90√2
- 90+3√2
Q. The volume of parallelopiped with vectors →a+2→b−→c, →a−→b, →a−→b−→c as coterminous edges is k[→a →b →c], then k is
- −2
- 2
- 3
- −3
Q. If →a, →b and →c are unit vectors, then the maximum value of |a−b|2+|b−c|2+|c−a|2 is
- 1
- 4
- 9
Q. Let →a and →b be two unit vectors inclined at an angle θ, then sin(θ2) is equal to
- 12∣∣^a−^b∣∣
- 12∣∣^a+^b∣∣
- ∣∣^a−^b∣∣
- ∣∣^a+^b∣∣
Q. Write two different vectors having same magnitude.
Q. The polar coordinate of a point P is (2, −π4). The polar coordinate of the point Q, which is such that the line joining PQ is bisected perpendicularly by the initial line, is
- (2, π4)
- (2, π6)
- (−2, π4)
- (−2, π6)
Q. If four vectors →a, →b, →c, →d are coplanar then (→a×→b)×(→c×→d) is equal to
- [→a →b →d]→c
- [→a →b →c]→d
- [→b →c →d]→a
- null vector
Q. Let (→p×→q)×→r+(→q⋅→r)→q=(x2+y2)→q+(14−4x−6y)→p and (→r⋅→r)→p=→r where →p and →q are two non-zero non-collinear vectors, and x and y are scalars. Then the value of (x+y) is
Q. Suppose the vectors X1, X2 and X3 are the solutions of the system of linear equations, Ax=b when the vector b on the right side is equal to b1, b2 and b3 respectively. if
X1=⎡⎢⎣111⎤⎥⎦, X2=⎡⎢⎣021⎤⎥⎦, X3=⎡⎢⎣001⎤⎥⎦, b1=⎡⎢⎣100⎤⎥⎦, b2=⎡⎢⎣020⎤⎥⎦ and b3=⎡⎢⎣002⎤⎥⎦, then the determinant of A is equal to
X1=⎡⎢⎣111⎤⎥⎦, X2=⎡⎢⎣021⎤⎥⎦, X3=⎡⎢⎣001⎤⎥⎦, b1=⎡⎢⎣100⎤⎥⎦, b2=⎡⎢⎣020⎤⎥⎦ and b3=⎡⎢⎣002⎤⎥⎦, then the determinant of A is equal to
- 2
- 12
- 32
- 4
Q.
Show that the vector ^i+^j+^k is equally inclined to the axes OX, OY and OZ.
Q. If ABCD is a quadrilateral such that −−→AB=^i+2^j and −−→AD=^j+2^k and −−→AC=2(^i+2^j)+3(^j+2^k). Then area of quadrilateral ABCD in sq. units is
- 5√212
- 3√212
- √212
- 72
Q. Let the vectors (2+a+b)^i+(a+2b+c)^j−(b+c)^k, (1+b)^i+2b^j−b^k and (2+b)^i+2b^j+(1−b)^k, a, b, c ∈R
be co-planar. Then which of the following is true ?
be co-planar. Then which of the following is true ?
- 3c=a+b
- 2b=a+c
- 2a=b+c
- a=b+2c
Q. A unit vector →a makes an angle of 45° with positive z−axis and if →a+^i+^j is a unit vector, then →a=
- (−12, −12, 1√2)
- (12, −12, 1√2)
- (12, 12, 1√2)
- (−12, −12, −1√2)
Q. If a, b and c are unit vectors, then |a−b|2+|b−c|2+|c−a|2 does not exceed
- 9
- 8
- 6
- 4
Q. In a △ABC, AB=AC, P and Q are points on AC and AB respectively such that CB=BP=PQ=QA. If ∠AQP=θ, then tan2θ is a root of the equation
- y3+21y2−35y−12=0
- y3−21y2+35y−12=0
- y3−21y2+35y−7=0
- 12y3−35y2+35y−12=0
Q. Find the unit vector in the direction of vector , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.
Q. A unit vector which is parallel to the tangent to the curve y2x−3x2=1 at (1, 2) is
- 1√5^i+2√5^j
- 1√5^i−2√5^j
- −2√5^i+1√5^j
- −2√5^i−1√5^j
Q. Which of the following is a unit vector
- (1, 1)
Q. If the area of the region bounded by the curve max(x, y)=1 and x2+y2=1 in first quadrant is a+πb sq.units. Then which of the following statement(s) is/are correct ?
- a−b=5
- a+b=9
- ab2>0
- a2b<0
Q. Show that each of the given three vectors is a unit vector: Also, show that they are mutually perpendicular to each other.
Q. The shortest distance between the lines x−33=y−8−1=z−31 and x+3−3=y+72=z−64 is:
- √30
- 2√30
- 5√30
- 3√30
Q. Consider the curves C1 and C2 given by C1:y=1+cosx and C2:y=1+cos(x–α) for α∈(0, π2), x∈[0, π]
The value of ′α′ for which the area of the figure bounded by the curves C1, C2 and x=0 is the same as that of the figure bounded by c2, y=1 and x=π is
The value of ′α′ for which the area of the figure bounded by the curves C1, C2 and x=0 is the same as that of the figure bounded by c2, y=1 and x=π is
- π3
- π4
- 5π12
- π6
Q. The value of x if x(^i+^j+^k) is a unit vector is
- ±1√3
- ±√3
- ±3
- ±13
Q. If is a nonzero vector of magnitude ‘ a ’ and λ a nonzero scalar, then λ is unit vector if (A) λ = 1 (B) λ = –1 (C) (D)
Q.
Given →A=0.3^i+0.4^j+c^k. Calculate the value of c if A is a unit vector.
0.75
0.87
0.96
0.45
Q. Which of the following is a unit vector in the direction of ^i+^j+^k.
- ^i+^j+k√3
- 13^i+1√3^j+1√3^k
- ^i+^j+^k√2
- None of these