Find a vector in the direction of the vector 5` hat i` - ` hat j` + 2` hat k` which has magnitude 8 units.

Find the unit vector in the direction of the vector vec a= hat i+ hat j+ 2 hat k .

Find a vector of magnitude 14 in the direction of the vector -3hat i+6 hat j-2 hat k .

Find the direction cosines of the vector hat i+2 hat j+3 hat kdot

Find a vector of magnitude 14 in the direciton of the vector -3hat(i)+6hat(j)-2hat(k) .

Find the direction cosines and direction ratios of the vector 2 hati + 2 hat j+5 hat k .

Find a unit vector in direction parallel to the sum of the vectors vec a = 2 hat i+4 hat j-5 hatk and vec b= hati+ 2 hat j+ 3hat k . Find also the direction cosines of this vector.

Find the angle of vector vec a = 6 hat i + 2 hat j - 3 hat k with x -axis.

Find the direction cosines and direction ratios of the vector 2hat(i)+3hat(j)+5 hat(k) .

Find a unit vector perpendicular to both the vectors 2 hat (i) - 3 hat (j) + 6 hat (k) and 3 hat (j) - 4 hat (k) . Also find the sine of the angle between the given vectors .

Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in the direction perpendicular to the direction of vector vec a= hat i+ hat j+ hat ki s hat i- hat jdot Statement 2: A component of vector in the direction of vec a= hat i+ hat j+ hat k is 2 hat i+2 hat j+2 hat kdot