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` .

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 veca=3hati+4hatj+5hatk and vecbeta =2hati+hatj-4hatk , then express vecbeta=vecbeta_1+vecbeta_2 such that vecbeta_1||vecalpha and vecbeta_2botvecalpha .

If a vector 2 hat i + 3 hat j + 8 hat k is perpendicular to the vector 4 hat j - 4 hat i + alpha hat k , then the value of alpha is

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

If vec(a) = 2 hat(i) + 3 hat (j) + 4 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - lambda hat(k) are perpendicular, then what is the value of lambda ?

If a vector (hat 2i+hat 3j+hat 8k) is perpendicular to the vector (hat 4i-hat 4j+hat alpha k) ,the value of alpha is

A point on the line hat r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

Find the values of a for which are vectors vecalpha= hat i+2 hat j+ hat k , vecbeta=a hat i+ hat j+2 hat k\ a n d\ vecgamma= hat i+2 hat j+a hat k are coplanar. \