Find the angle between the unit vectors `hata and hatb `given that `| hata + hatb |=1`

If the angle between the unit vectors hata " and " hatb is 60^(@) , the |hata-hatb| is :-

Find the angle between two vectors hatA=2hati+hatj-hatk and hatB=hati-hatk

Let hata,hatb and hatc be unit vectors and alpha, beta , and gamma the angles between the vectors hata,hatb,hatb,hatc and hatc, hata respectively . If hata + hatb+hatc is also a unit vectors, then cosalpha + cosbeta +cosgamma is equal to -

Find the angle between unit vector veca and vecb so that sqrt(3) veca - vecb is also a unit vector.

Unit vector hata and hatb are perpendicular to each other and the unit vector hatc is inclined at an angle theta to both hata and hatb If hatc=m(hata+hatb)+hatn(hata times hatb) . And m,n are real prove that pi/4 le theta le (3pi)/4 .

The vector veca+vecb bisects the angle between the vectors hata and hatb if (A) |veca|+|vecb|=0 (B) angle between veca and vecb is zero (C) |veca|=|vecb|=0 (D) none of these

If hata,hatb and hatc are three unit vectors such that hata + hatb + hatc is also a unit vector and theta_(1),theta_(2) and theta_(3) are angles between the vectors hata,hatb,hatb,hatc and hatc,hata, respectively m then among theta _(1),theta_(2)and theta_(3)

Assertion : Suppose hata,hatb,hatc are unit vectors such that hata,hatb=hata.hatc=0 and the angle between hatb and hatc is pi/6 than he vector hata can be represented as hata=+-2(hatbxxhatc), Reason: hata=+-(hatbxxhatc)/(hatbxxhatc|) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If hata and hatb are two unit vectors and theta is the angle between them then vector 2hatb+hata is a unit vector if (A) theta= pi/3 (B) theta=pi/6 (C) theta=pi/2 (D) theta=pi