Question

What vector must be added to the sum of two vector 2i+j+3k and 3i-2j-2k so that the resultant is a unit vector along Z axis

Answer 1

let A=2i+j+3k and B=3i-2j-2k and A+B=C. so, C= (2+3)i+(1-2)j+(3-2)k ie, 5i-j+k. Now, let D be added to vector C such that it gives k, which is unit vector along Z axis. so, D+[ 5i-j+k ]= k. Or D= k-[5i-j+k ]which gives us D= -5i+j.

Answer 2

Unit vector along Z -axis is = k

Given,

2i+j+3k = A (let)

3i-2j-2k = B (let)

Let, C = xi+yj+zk be the new vector to be added to the sum of A and B.

According to the question:

( 2+3+x)i + ( 1-2+y)j + (3-2+z)k = k

Comparing the coefficients on both the sides,

5+x = 0 ⇒x =-5

-1 +y = 0⇒y=1

1+z = 1⇒z =0

Therefore, C = -5i + j