If and find a vector of magnitude 6 units which is parallel to the vector

OR

Let and Find a vector which is perpendicular to both and and

Given,

To Find: Find a vector which is parallel to

Explanation:

And, Let Assume

So,

Since ,

Now,

The magnitude of the required vector is 6 units given, then

Hence, The required vector is

OR

Given,

To find: Find a vector d which is perpendicular to both

Explanation: we have

and, is perpendicular to both

Since, - - - (i)

And, - - - (ii)

Let us Assume vector

Therefore,

X + 4y + 2z = 0

Also,

3x - 2y + 7z = 0

On solving the above equation,

It is given that

2x - y + 4z = 18

2(32p) - ( - p) + 4( - 14p) = 18

64p + p - 56p = 18

9p = 18

p = 2

So, That x = 64 , y = - 2 , z = - 28

Therefore,

Hence, The vector