+91-93193 64476
FlagBACK
Flag Vectors> A unit vector in xy-plane that makes an a...
question mark

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...

Pritesh , 11 Years ago
Grade
anser 5 Answers
Y RAJYALAKSHMI
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
 
 
 
 
ApprovedApproved
Last Activity: 11 Years ago
Pritesh
Sir, Thankyou for your Reply but sir
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...
Last Activity: 11 Years ago
Y RAJYALAKSHMI
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’
 
 
Last Activity: 11 Years ago
Pritesh
Thankyou Sir......
Last Activity: 11 Years ago
Ankit Jaiswal
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
 
Last Activity: 10 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on vectors

question mark
A body is rotating with an angular velocity of 2radians per second about the line joining (1, 2,3) and (2, 3,5) find the velocity of the particle of the body which is momentarily at (3, 5,6) 
 
vectors
1 Answer Available

Last Activity: 4 Years ago

question mark
Show that: vectorPQ+vectorPR+ vectorPS +vectorTP+vectorUP = 4PQ
Vector
vectors
1 Answer Available

Last Activity: 4 Years ago

question mark
Given that A×(B×C) = (A.C)B - ( A.B)C , deduce that (A×B)×C = (A.C)B - (B.C)A
vectors
1 Answer Available

Last Activity: 4 Years ago

question mark
the mean of 30 observations was 17 with sd2. later it was found that two of the observations were incorrect, which were recorded as 19vand 21.find the correct sd if the incorrect values are deleted and correct values 22 and 15 are included
vectors
1 Answer Available

Last Activity: 4 Years ago

question mark
Find the component of 2i +3j +k in the direction of 3i-j 
 
vectors
1 Answer Available

Last Activity: 4 Years ago