Mechanics> With respect to a rectangular Cartesian c...

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!

Grace Mathew , 9 Years ago

Grade 11

1 Answers

Manas Shukla

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 / $\sqrt{3}$

Approved

Last Activity: 9 Years ago

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Mechanics> With respect to a rectangular Cartesian c...

Grace Mathew , 9 Years ago

Manas Shukla

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