The angles which the vector i^+j^+rt2k^ makes withe X,Y and Z axes respectively are

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)