Question

Find
the
vector
which the
angles
î -ị+√2k
makes
with the coordinate
auces.​

Answer 1

becuase dot product of two vectors is equal to product of magnitude of two vectors and cos of the angle between them. that is A.i=|A||i|cosX

.magnitude of A = sqareroot(1+1+2) = sqareroot(4) = 2. A.i(on expanding) = i.i+i.j+i.sqareroot(2)k = 1+0+0 = 1. |i| = 1. therefore A.i =1 and |A|.|i| = 2. overall result will be

A.i=|A||i|cosX

=>1=2cosX

=>X=60⁰

Or

Let the unit vector along x axis be i(cap)

i+j+√2k=A is the given vector

A.i=|A||i|cosX

=>1=2cosX

=>X=60⁰ (angle made with the X axis) 

Let the unit vector along y axis be j(cap)

A.j=|A||j|cosY

=>Y=60⁰ (angle made with the Y axis)

Let the unit vector along z axis be k(cap)

A.k=|A||k|cosZ

=>√2=2cosZ

=>Z=45⁰ (angle made with the Z axis)

Hope this will help you.....

My best.....