Let the vectors `veca,vecbvecc` be given as `a_(1)hati+a_(2)hatj+a_(3)hatk,b_(1)hati+b_(2)hatj+b_(3)hatkc_(1)hati+c_(2)hatj+c_(3)hatk`. Then show that `vecaxx(vecb+vecc)=vecaxxvecb+vecaxxvecc`

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati + b_(2)hatj + b_(3)hatk and vecc=c_(1)hati +c_(2)hatj +c_(3)hatk be three non-zero vectors such that vecc is a unit vector perpendicular to both vectors, veca and vecb . If the angle between veca and vecb is pi//6 "then" |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|^(2) is equal to

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati+b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk be three non-zero vectors such that vecc is a unit vector perpendicular to both veca and vecb . If the angle between veca and vecb is pi//6 then the value of |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|"is"

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati+b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk be three non-zero vectors such that vecc is a unit vector perpendicular to both veca and vecb . If the angle between veca and vecb is pi//6 then the value of |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|"is"

Statement 1: If a_(1)hati + a_(2)hatj + a_(3)hatk, vecbhati+b_(2)hatj + b_(3) hatk and c_(1)hati + c_(2)hatj + c_(3)hatk are three mutually perpendicular unit vectors then a_(1)hati + b_(1)hatj + c_(1)hatk,a_(2)hati +b_(2)hatj+c_(2) hatk and a_(3)hati + b_(3) hatj + c_(3) hatk may be mutually perpendicular unit vectors. Statement 2 : value of determinant and its transpose are the same.

If veca=hati-2hatj+3hatk and vecb=-2hati+hatj-2hatk , then the value of |veca xx vecb| is -

If veca = hati + hatj + hatk , vecb = hatj - hatk then find a vector vecc , such that veca xx vecc = vecb and veca .vecc = 3 .

If vecA= 5hati+6hatj+3hatk and vecB=6hati-2hatj-6hatk , then

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the vector vecc such that veca.vecc =2 and veca xx vecc=vecb .

Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, veca botvecb,veca.vecc=4 then find the value of [(veca, vecb, vecc)] .