What is the unit vector parallel to ` vec a=3 hat i+4 hat j-2 hat k` ? What vector should be added to ` vec a` so that the resultant is the unit vector ` hat i ?`

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

Find the unit vector perpendicular to the plane vec r.(2 hat i+ hat j+2 hat k)=5.

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

Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b= hat i+2 hat j-4 hat kdot Find the unit vector in the direction of the resultant vector.

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

Vectors vec a= hat i+2 hat j+3 hat k , vec b=2 hat i- hat j+ hat k and vec c=3 hat i+ hat j+4 hat k , are so placed that the end point of one vector is the starting point of the next vector. Then the vector are (A) not coplanar (B) coplanar but cannot form a triangle (C) coplanar and form a triangle (D) coplanar and can form a right angled triangle

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.

Vector 1/3(2hati-2hatj+hatk) is (A) a unit vector (B) makes an angle pi//3 with vector (2 hat i-4 hat j+3 hat k) (C) parallel to vector (- hat i+ hat j-1/2 hat k) (D) perpendicular to vector 3 hat i+2 hat j-2 hat k

find the projection of the vector vec a=2hat i+3 hat j+2 hat k , on the vector vec b=hati+2hatj+hat k

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .