Addition and Subtraction in Unit Vector Notation
Trending Questions
If A=3^i+4^j and B=7^i+24^j, the vector having the same magnitude as B and parallel to A is
5^i+20^j
15^i+10^j
20^i+15^j
15^i+20^j
Two forces \(\vec{F_1}=5\hat{i}+10\hat{j}-20\hat{k}\) and →F2=10^i−5^j−20^k act on a single point. The angle between →F1 and →F2 is nearly
30∘
45∘
60∘
90∘
Can the scalar product of two vectors be a negative quantity?
- 18^i−6^j
- 32^i−13^j
- −18^i+6^j
- −25^i+13^j
Surface area is
Scalar
Vector
Neither scalar nor vector
Both scalar and vector
Find the unit vector in the direction opposite to the direction of the vector 6^i−8^j+10^k
−6^i+8^j−10^k
(−610)^i+(810)^j−(1010)^k
(−6√200)^i+(8√200)^j−(10√200)^k
None of these.
If a particle moves from point P (2, 3, 5) to point Q (3, 4, 5). Its displacement vector be
^i+^j+10^k
^i+^j+5^k
^i+^j
2^i+4^j+6^k
If A=3^i+4^j and B=7^i+24^j, the vector having the same magnitude as B and parallel to A is
5^i+20^j
15^i+10^j
20^i+15^j
15^i+20^j
An object of m kg with speed of v m/s strikes a wall at an angle q and rebounds at the same speed and same angle. The magnitude of the change in momentum of the object will be
2mv cosθ
2mv sinθ
0
2mv
What vector must be added to the two vectors ^i−2^j+2^kand2^i+^j−^k, so that the resultant may be a unit vector along x-axis
2^i+→j−→k
−2^i+→j−→k
2^i−→j+→k
−2^i−→j−→k
- A√3
- A√2
- √3A
- √3A
- 4^i+2^j+5^k
- −4^i−2^j+5^k
- 3^i+4^j+5^k
- Null vector
Vectors A and B are 6^i−7^j+6^k and 3^i+4^j+6^k respectively. Their vector difference in unit vector notation will be
9^i−3^j+12^k
9^i−11^j+12^k
10^i−^j−^k
3^i−11^j+0^k
With respect to a rectangular cartesian coordinate system, three vectors are expressed as →a=4^i−^j, →b=−3^i+2^j and
→c=−^k where ^i, ^j, ^k are unit vectors, along the X, Y and Z-axis respectively. The unit vectors ^ralong the direction of sum of these vector is
^r=1√3(^i+^j−^k)
^r=1√2(^i+^j−^k)
^r=1√3(^i−^j+^k)
^r=1√2(^i+^j+^k)
Can we add 2 vectors of unequal magnitudes and get a zero vector?
True
False
- 4^i+6^j
- 4^i−^j
- −4^i+6^j
- −4^i−6^j
Given that →A+→B=→C and that →C is ⊥ to →A. Further if |→A|=|→C|, then what is the angle between →A and →B
π4radian
π2radian
3π4radian
πradian
Magnitude of vector which comes on addition of two vectors, 6^i+7^j and 3^i+4^j is
√136
√13.2
√202
√160
Given that 0.2^i+0.6^j+a^k is a unit vector. What is the value of a?
√0.3
√0.4
√0.6
√0.8
If →A=4^i−3^j and →B=6^i+8^j then magnitude and direction of →A+→B will be
5, tan−1(34)
5√5, tan−1(12)
10, tan−1(5)
25, tan−1(34)
- ^r=1√3(^i+^j−^k)
- ^r=1√2(^i+^j−^k)
- ^r=13(^i+^j−^k)
- ^r=1√3(^i+^j+^k)
Two forces, →F and →F2 are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is
cos−1(12)
cos−1(−12)
cos−1(−14)
cos−1(14)
Two forces, →F and →F2 are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is
cos−1(12)
cos−1(−12)
cos−1(−14)
cos−1(14)
- 2 cm along + y - axis
- 2√3 cm along + y - axis
- 1 cm along - x- axis
- 2 cm along - x - axis
Add vectors A & D. Which of these is the correct result?
4^i
0^i
−1^i
None of these
The angle between the two vectors →A=3^i+4^j+5^k and →B=3^i+4^j−5^k will be
90∘
0∘
60∘
45∘
Surface area is
Scalar
Vector
Neither scalar nor vector
Both scalar and vector
The position vector of a particle is →r=(a cos ωt)^i+(a sin ωt)^j. The velocity of the particle is
Parallel to the position vector
Perpendicular to the position vector
Directed towards the origin
Directed away from the origin
The position vector of a particle is determined by the expression
→r=3t2^i+4t2^j+7^k. The distance traversed in first 10 sec is
500 m
300 m
150 m
100 m
- ^r=1√3(^i+^j−^k)
- ^r=1√2(^i+^j−^k)
- ^r=13(^i+^j−^k)
- ^r=1√3(^i+^j+^k)
