+91-87964 74404
FlagBACK
Question icon
Grade 10Vectors

a and b are two unit vector mutually perpendicular. Find a unit vector equally inclined to a,b,a×b

Profile image of Rivu
7 Years agoGrade 10
Answers icon

1 Answer

Profile image of Arun
7 Years ago
 
we have c =xa + yb +z (a x b)
c.a = x
and 
c.b = y
hence x = y = cos theta
 
now c.c = c^2
(xa + yb +z (a x b)).(xa + yb +z (a x b)) =  |c|^2
 
2 x^2 +z^2 |a|^2 |b|^2 – (a.b)^2 = 1
2 x^2 + z^2 – 0 = 1
since a and b are perpendicular to each other
 
hence z^2  = 1 – 2x^2 = 1- 2 cos^2theta = – cos 2\theta

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