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Grade: 11

                        

With respect to a rectangular Cartesian coordinate system, three vectors are expressed as ‘a’ vector=4icap-jcap , ‘b’ vector=-3icap + 2jcap and c vector = -kcap where icap,jcap and kcap are unit vectors along X,Y and Z axes respectivelu. The unit vector r along the direction of the sum of these three vectors is rcap = (icap+jcap-kcap) (1/√3) ---answer rcap = (icap+jcap-kcap) (1/√2) rcap = (icap-jcap+kcap) (1/√3) rcap = (icap+jcap+kcap) (1/√3) rcap = (icap-jcap+kcap) (1/√2) How do you get this answer? Thanks!

4 years ago

Answers : (1)

Manas Shukla
102 Points
							
First thing to note in this question is unit vector which is defined as
unit vector = \frac{\underset{r}{\rightarrow}}{\left | \underset{r}{\rightarrow} \right |}
so here resultant = vector a + vector b + vector c
R = 4i – j – 3i +2j – k = i + j – k
now modulus of R = \sqrt{x^{2}+y^{2}+z^{2}}
where R = xi + yj + zk
Now for this problem
unit vector = i + j – k / \sqrt{3}
4 years ago
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