NIMCET 2020 Question Paper with solutions

Question : 32 of 120

Marks: +1, -0

a↖{r},b↖{r},c↖{r},d↖{r}

are four vectors such that

a↖{r}+b↖{r}+c↖{r}

is collinear with

d↖{r}

and

b↖{r}+c↖{r}+d↖{r}

is collinear with

a↖{r}

,then

a↖{r}+b↖{r}+c↖{r}+d↖{r}

Solution:

a+b+c=λd

a+b+c+d=(λ+1)d

........(1)

b+c+d=λa

a+b+c+d=(λ+1)a

.....(2)
from (1) & (2)

(λ+1)d=(λ+1)a

a↖{r}+b↖{r}+c↖{r}+d↖{r}=0↖{r}

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