If ` vecalpha=3 hat i+4 hat j+5 hat k` and ` vecbeta=2 hat i+ hat j-\ 4 hat k ,` then express ` vecbeta` in the form ` vecbeta_1+ vecbeta_2,` where ` vecbeta_1\ ` is parallel to ` vecalpha` and ` vecbeta` is perpendicular to ` vecalpha` .

If vecalpha=3 hat i+4 hat j+5 hat k and vecbeta=2 hat i+ hat j-4 hat k , then express vecbeta in the form of vecbeta= vecbeta_1+ vecbeta_2, where vecbeta_1 is parallel to vecalpha and vecbeta_2 is perpendicular to vecalpha .

If vecalpha=3 hat i+4 hat j+5 hat k\ a n d\ vecbeta=2 hat i+ hat j-4 hat k , then express vecbeta in the form of vecbeta= vecbeta_1+ vecbeta_2w h e r e\ vecbeta_1 is parallel to vecalpha\ a n d\ vecbeta_2 is perpendicular to vecalphadot

If with reference to the right handed system of mutually perpendicular unit vectors hat i , hat j and hat k , vecalpha=3 hat i- hat j , vecbeta=2 hat i+ hat j-3 hat k , then express vecbeta in the from vecbeta=vecbeta_1+ vecbeta_2 , where vecbeta_1 is parallel to vecalpha and vecbeta_2 is perpendicular to vecalpha

If with reference to a right handed system of mutually perpendicular unit vectors hat i ,\ hat j ,\ hat k we have vecalpha=3 hat i- hat j ,\ a n d\ vecbeta=2 hat i+ hat j-3 hat kdot Express vecbeta in the form vecbeta= vecbeta_1+ vecbeta_2,\ w h e r e\ vecbeta_1 is parallel to vecalpha\ a n d\ vecbeta_2 is perpendicular to vecalphadot

Let vecalpha = 3hati + hatj and beta= 2hati - hatj + 3hatk . If vecbeta = vecbeta_(1) - vecbeta_(2) , where vecbeta_(1) is parallel to vecalpha and vecbeta_(2) is perpendicular to vecalpha , then vecbeta_(1) xx vecbeta_(2) is equal to:

if vectors 3 hat i - 2 hat j + m hat k and - 2 hat i+ hat j+ 4 hat k are perpendicular to each other , find the value of m

If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and vec c= hat i+2 hat j- hat k , find |3 vec a-2 hat b+4 hat c|dot

Let vecalpha=a hat i+b hat j+c hat k , vecbeta=b hat i+c hat j+a hat ka n d vecgamma=c hat i+a hat j+b hat k are three coplanar vectors with a!=b ,a n d vec v= hat i+ hat j+ hat kdot Then v is perpendicular to vecalpha b. vecbeta c. vecgamma d. none of these

Given vecalpha=3 hat i+ hat j+2 hat ka n d vecbeta= hat i-2 hat j-4 hat k are the position vectors of the points Aa n dBdot Then the distance of the point - hat i+ hat j+ hat k from the plane passing through B and perpendicular to A B is a. 5 b. 10 c. 15 d. 20

If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat k and vec gamma=c hat i+c hat j+b hat k are coplanar, then prove that c is the geometric mean of a and b.