[" If the vectors "vec x=hat f+2vec f+3hat k,vec y=2vec i-vec j+4hat k" and a is a vector such that a "perp" a and "],[:.quad 4" ,then a "=]

If for a vector vec a , vec a*hat i = vec a*hat j= vec a*hat k=0 , then find |vec a| .

If vec a=hat i+2hat j-3hat k and vec b=2hat i+4hat j+9hat k find a unit vector parallel to vec a+vec b

Find the angle between the vectors vec a and vec b where: vec a=2hat i-hat j+2hat k and vec b=4hat i+4hat j-2hat k

Find the angle between the vectors vec a and vec b where: vec a=2hat i-hat j+2hat k and vec b=4i+4hat j-2hat k

A vector vec C when added to the resultant of the vectors vec A = 3 hati -4 hat j + 5 hat k and vec B = 2 vec 2 hat I + 3 hat j -4 hat k giv es a unit vector along y-axis. Find the magnitude of vec C .

If vec a=4 hat i -hat j +hat k and vec b =2hat i-2 hat j+hat k , then find a unit vector vec a+ vec b .

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k

Find the angle between the vectors vec a and vec b where: vec a=2hat i-3hat j+hat k and vec b=hat i+hat j-2hat k

Find the angle between the vectors vec a and vec b where: vec a=3hat i-2hat j-jhat k and vec b=4hat i-hat j+8hat k

If vec a=hat i+hat j+hat k and vec b=hat j-hat k, find a vector vec c such that vec a x vec c=vec b and vec a*vec c=3