Vector `p= 4i - j + 8k` and `q = 2i - mj + 4k`. Find the value of m if p and q have same direction.​

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

Consider the vectors a = i- 2j + k and b= 4i- 4j + 7k What is the vector perpendicular to both the vectors?

If vectors 2i - j + k, i + 2j - 3k and 3i + mj + 5k are coplanar, then m is a root of the equation

Let a=2i+4j-5k , b=i+j+k and c=j+2k .Find the unit vector in the opposite direction of a+b+c

If vec p=5vec i+lambdavec j-3vec k and vec q=vec i+3vec j-5vec k ,then find the value of lambda, so that vec p+vec q and vec p-vec q are perpendicular vectors.

If p=5hat i+lambdahat j-3hat k and vec q=hat i+3hat j-5hat k then find the value of lambda such that vec p+vec q and vec p-vec q are perpendicular vectors.

The sides of a parallelogram represented by vectors p = 5hat(i) - 4hat(j) + 3hat(k) and q = 3hat(i) + 2hat(j) - hat(k) . Then the area of the parallelogram is :

If bar a=hat i+hat j-4hat k and bar(b)=hat 4i-hat j-2hat k then find (i) a unit vector in the direction of the vector (2bar(a)-bar(b))