# Vector Notation

## Trending Questions

**Q.**

How do you find the angle of resultant vector?

**Q.**The angle made by vector 3^i+3^k with x-axis & y-axis respectively are

- 45∘, 90∘
- 90∘, 90∘
- 45∘, 45∘
- 30∘, 60∘

**Q.**

A cart of mass $\mathrm{M}$ has a block of mass **m** attached to it, the coefficient of friction between the block and the cart is $\mathrm{\xce\xbc}$. What is the maximum acceleration of the cart so that the block m does not fall $\left(\mathrm{a}\right)$

$\frac{\mathrm{\xce\xbc}}{\mathrm{g}}$

$\mathrm{\xce\xbcg}$

$\frac{\mathrm{g}}{\mathrm{\xce\xbc}}$

$\frac{\mathrm{M\xce\xbcg}}{\mathrm{m}}$

**Q.**

What is the $\mathrm{cos}\left({53}^{\xc2\xb0}\right)$?

**Q.**An observer O is moving with the velocity 3 m/s in the direction as shown in the figure. Find the time till the observer will be able to see his image in the plane mirror placed at an angle of 60∘ with the horizontal.

- 2 sec
- 1 sec
- 4 sec
- 6 sec

**Q.**

Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y=2x2 and the slope of tangent is tan θ=dydx=4x.

x12345678910y281832507298128162200

**Q.**The

**speed of the boat in still water is**

**20 m/s**

**and the speed of river flowing due east is**

**10 m/s. If the boat is on the southern end and it has to cross the river**

**along the shortest path, then the angle at which it should move with respect to north is**

30° west

0°

45° west

60° west

**Q.**Find the component of vector →A=(2∧i+∧3j) along the direction (∧i+∧j).

- −5√2(∧i−∧j)
- −12(∧i+∧j)
- 12(∧i−∧j)
- 5√2(∧i+∧j)

**Q.**

In the figure shown, explain the difference between $\stackrel{\xe2\u2020\u2019}{DE}$ and $\stackrel{\xe2\u2020\u2019}{ED}$.

**Q.**A particle is moving such that its position coordinates (x, y) are

(2m, 3m) at time t=0,

(6m, 7m) at time t=2 s and

(13m, 14m) at time t=5 s.

Average velocity vector (→Vav) from t=0 to t=5 s is:

- 15(13^i+14^j)
- 73(^i+^j)
- 2(^i−^j)
- 115(^i+^j)

**Q.**If vectors →A=cosωt^i+sinωt^j and →B=cosωt2^i+sinωt2^j are functions of time, then the value of t at which they are orthogonal to each other is :

- t=0
- t=π4ω
- t=π2ω
- t=πω

**Q.**The negative of vectors can also be thought of as equal vectors, with their positive counterparts.

- True
- False

**Q.**The force F is exerted on a particle of mass 5 kg. If the particle starts from rest from origin and its position after 3 s is (4.5^i+13.5^j)m, then find →F.

- (5^i+13.5^j)N
- (5^i+15^j)N
- (5^i+13^j)N
- (15^i+5^j)N

**Q.**Let F(x)=∫x2+π6x2cos2tdt for all xϵR and f:[0, 12]→[0, ∞) be a continuous function. For αϵ[0, 12], if F′(a)+2 is the area of the region bounded by x=0, y=0, y=f(x) and x=a, then f(0) is

**Q.**Give the derivation for resultant of two vectors and for the angle between resultant and a vector.

**Q.**Resultant of three non-coplanar non-zero vectors ¯¯¯a, ¯¯b and ¯¯c :

- always lies in the plane containing ¯¯¯a+¯¯b
- always lies in the plane containing ¯¯¯a−¯¯b
- can be zero
- cannot be zero

**Q.**Negative vectors are delocalised in nature.

- False
- True

**Q.**

Vector →A=5^i+4^j+3^k is rotated around Z-axis such that its projection on the x-y plane is rotated through 180∘.Choose the correct option?

No it won't as translation of a vector doesn't change it

Yes, New Vector =

No, it won't as the angle is

Yes, New vector =

**Q.**Two points A and B in space have the co-ordinates (2, −1, 3) and (4, 2, 5) respectively. Find vector AB.

**Q.**A force →F=6→i−8→j+10→k N produces an acceleration of magnitude 1ms−2 in a body, the mass of the body would be:

- 200kg
- 6√2kg
- 10√2kg
- 20kg

**Q.**The angle that the vector →A=2^i+3^j makes with x-axis is

- tan−1(3/2)
- tan−1(2/3)
- sin−1(2/3)
- cos−1(3/2)

**Q.**A vector →a has components 2p and 1 with respect to a reactangular cartesian system. The system is rotated through a certain angle about the origin in the counterclockwise direction . If with respect to the new system, →a has componets p+1 end 1 then.

**Q.**A vector is inclined at π4 rad with x-axis & π3 rad with y-axis then find angle of vector with z-axis.

- 5π3 rad
- 2π3 rad
- π2 rad
- π4 rad

**Q.**State whether True or False :

Motion in 3-Dimension can't be represented with the help of vectors.

- True
- False

**Q.**Resolve a weight of 10 N in two directions which are parallel an perpendicular to a slope inclined at 30 to the horizontal,

**Q.**The rectangular components of a vector lying in xy plane are (n + 1) and 1. If coordinate system is turned by 600. They are n and 3 respectively the value of 'n'.

- 3
- 3.5
- 4
- 4.5

**Q.**Draw a graph from the following data. Draw tangents at x=2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y=2x2 and the slope of tangent is tanθ=dydx=4x.

x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

y | 2 | 8 | 18 | 32 | 50 | 72 | 98 | 128 | 162 | 200 |

**Q.**An airplane is heading north east at a speed of 141ms−1. The northward component of its velocity is:

- 141.4ms−1
- Zero
- 50ms−1
- 100ms−1

**Q.**Vector is represented by directed line segment where length of line gives ___________ of vector.

- Direction
- Magnitude
- Both (A) and (B)
- None of the above.

**Q.**Explain the resolution of vectors in two dimensions.