# A unit vector in xy-plane that makes an angle of 45(degree) with the vector i(cap)+j(cap) and an angle of tan(inverse)(4/5) with the vector 3(icap)-4(jcap) is...

Y RAJYALAKSHMI
45 Points
9 years ago
The vector in xy plane is ai + bj
Since it is a unit vector we have a^2 + b^2 = 1  --------  (1)
The angle made by the vector ai + bj & i + j
cos 45 = (a*1 + b*1)/sq root(a^2 + b^2) * sq root (1^2 + 1^2) ----------- (2)
The angle made by the vector ai + bj & 3i – 4j is tan^-1 (4/5) = > cos^-1(5/sq root 41)
5/sq root (41) = (a * 3 – b * 4) / sq root(a^2 + b^2) * sq root (3^2 + 4^2)  -------- (3)

Solve for a, b using these 3 equations

Pritesh
24 Points
9 years ago
i. a^2 + b^2 = 1
ii.1^2 + 1^2
iii.a*1 + b*1
what is this stand for I dont know...means its 2ai(cap) or something else...
Y RAJYALAKSHMI
45 Points
9 years ago
I did not write (cap)  for vector so that we do not get confused with thest signs.
^  means square  ----- a^ 2 means  ‘a square’
* means multiplication ------  a * 1 means ‘ a multiplied by 1’

Pritesh
24 Points
9 years ago
Thankyou Sir......
Ankit Jaiswal
165 Points
8 years ago
hi

The vector in xy plane is ai + bj
Since it is a unit vector we have a^2 + b^2 = 1  --------  (1)
The angle made by the vector ai + bj & i + j
cos 45 = (a*1 + b*1)/sq root(a^2 + b^2) * sq root (1^2 + 1^2) ----------- (2)
The angle made by the vector ai + bj & 3i – 4j is tan^-1 (4/5) = > cos^-1(5/sq root 41)
5/sq root (41) = (a * 3 – b * 4) / sq root(a^2 + b^2) * sq root (3^2 + 4^2)  -------- (3)

Solve for a, b using these 3 equations