Home
Class 11
PHYSICS
If vec(A)=4hat(i)-3hat(j) and vec(B)=6ha...

If `vec(A)=4hat(i)-3hat(j)` and `vec(B)=6hat(i)+8hat(j)`,then find the magnitude and direction of `vec(A)+vec(B)`.

A

`5, tan^(-1) (3//4)`

B

`5 sqrt5, tan^(-1) (1//2)`

C

`10, tan^(-1) (5)`

D

`25, tan^(-1) (3//4)`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(A) + vec(B) = 4hat(i) - 3hat(j) + 6hat(i) + 8 hat(j)= 10 hat(i) + 5hat(j)`
Magnitude `- |vec(A) + vec(B)|= sqrt(10^(2) + 5^(2))= sqrt125 = 5 sqrt5`
`tan theta= (5)/(10) rArr theta= tan^(-1) (1//2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If vec(A) = 3 hat(i) - 4 hat(j) and vec(B) = 2 hat(i) + 16 hat(j) then the magnitude and direction of vec(A) + vec(B) will be

Which of the following is not true ? If vec(A) = 3hat(i) + 4hat(j) and vec(B) = 6hat(i) + 8hat(j) where A and B are the magnitude of vec(A) and vec(B) ?

If vec(A)=2hat(i)+3hat(j)-hat(k) and vec(B)=-hat(i)+3hat(j)+4hat(k) , then find the projection of vec(A) on vec(B) .

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+2hat(j)+2hat(k) , find the magnitude of compinent of (vec(A)+vec(B)) along vec(B)

If vec a=2hat i-2hat j+hat k,vec b=2hat i+3hat j+6hat k and vec c=-hat i+2hat k then find the magnitude and direction of the vector vec a-vec b+2c

vec(A)=(3hat(i)+2hat(j)-6hat(k)) and vec(B)=(hat(i)-2hat(j)+hat(k)) find the scalar product of vec(A) and vec(B) .

IF vec(A) = 5hat(i) + 12hat(j) and vec(B) = 3hat(i) + 4hat(j) , find component of vec(A) in the direction of vec(B) .

If vec(A)=4hat(i)+nhat(j)-2hat(k) and vec(B)=2hat(i)+3hat(j)+hat(k) , then find the value of n so that vec(A) bot vec(B)

If vec(b)=3hat(i)+4hat(j) and vec(a)=hat(i)-hat(j) the vector having the same magnitude as that of vec(b) and parallel to vec(a) is