Home
Class 12
PHYSICS
Find the component of vector A+B along ...

Find the component of vector A+B along
i. X-axis, ii. C.
Given, `A=hat(i)-2hat(j)+3hat(k)andC+hat(i)+hat(j).`

A

`3,(1)/(sqrt(2))`

B

`2,(3)/(sqrt(2))`

C

`5,(2)/(3)`

D

`4.1, (2)/(sqrt(2))`

Text Solution

Verified by Experts

`(a) A+B=(hat(i)-2hat(j))+(2hat(i)+3hat(j))=3hat(i)-2hat(j)+3hat(k)`
i. Component of A+B along X -axis is 3.
ii. Component of A+B=R (say) along C is
`:. R*C=RC cos theta`
`Rcostheta+(R*C)/C=((31hati-2hat(j)+3hat(k))*(hati+hat(j)))/sqrt((1)^(2)+(1)^(2))`
`=(3-2)/(sqrt(2))=(1)/(sqrt(2))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SCALARS AND VECTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 1|37 Videos

  • SCALARS AND VECTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (Miscellaneous Problems)|20 Videos

  • ROTATIONAL MOTION'

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|35 Videos

  • SEMICONDUCTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|25 Videos

Similar Questions

Explore conceptually related problems

Find the components of vector vec(a)=3hat(i)+4hat(j) along the direction of vectors hat(i)+hat(j) & hat(i)-hat(j)

hat(i) and hat(j) are unit vectors along x-and y-axes respectively. What is the magnitude and the direction of the vectors hat(i)+hat(j) and hat(i)-hat(j) ? What are the components of a vector vec(A)=2hat(i)+3hat(j) along the direction hat(i)+hat(j) and hat(i)-hat(j) ?

Knowledge Check

  • The component of vector A= 2hat(i)+3hat(j) along the vector hat(i)+hat(j) is

    A
    `5/(sqrt(2))`
    B
    `10sqrt(2)`
    C
    `5sqrt(2)`
    D
    5

  • The two vectors A=2hat(i)+hat(j)+3hat(k) and B=7hat(i)-5hat(j)-3hat(k) are :-

    A
    parallel
    B
    perpendicular
    C
    anti-parallel
    D
    None of these

  • The vector component of vector vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k) along vector vec(B) = hat(i) + hat(j) + hat(k) is

    A
    `2 hat (i) + 2 hat(j) + 2 hat(k)`
    B
    `3 hat (i) + 3 hat(j) + 3 hat(k)`
    C
    `4 hat (i) + 4 hat(j) + 4 hat(k)`
    D
    `5 hat (i) + 5 hat(j) + 5 hat(k)`

    • Similar Questions

    Explore conceptually related problems

    Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

    Find the component of a vector vec A = 3 hat I + 4 hat j along the direction of 2hat I -3 hat j .

    Find the vector projection of the vector : 2hat(i)-hat(j)+hat(k) on hat(i)-2hat(j)+hat(k) .

    Express -hat(i)-3hat(j)+4hat(k) as the linear combination of the vectors 2hat(i)+hat(j)-4hat(k) , 2hat(i)-hat(j)+3hat(k) and 3hat(i)+hat(j)-2hat(k) .

    Find the component of a vectro vec A = 3 hat I + 2 hat j along the direction of ( hat I + hat j)

    Home
    Profile