NIMCET 2021 Question Paper with solutions

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Question : 38 of 120

Marks: +1, -0

Let

{a}↖{→}=i+j

and

{b}↖{→}=2 i-k

. Then the point of intersection of the lines

{r}↖{→} \×{a}↖{→}={b}↖{→} \× {a}↖{→}

and

{r}↖{→} \×{b}↖{→}={a}↖{→} \×{b}↖{→}

is

$-{i}+{j}+{k}$
$3 {i}-{j}+{k}$
${i}-{j}-{k}$
$3 {i}+{j}-{k}$

Solution:

{r}↖{→} \×{a}↖{→}={b}↖{→} \× {a}↖{→}

........(1)

{r}↖{→} \×{b}↖{→}={a}↖{→} \×{b}↖{→}

.......(2)
Adding equation (1) and (2)

r \×a+r \×b=b \×a+a \ × b

r \×(a+b)=-(a \×b)+(a \×b)

r \×(a+b)=0

r \×[(i+j)+(2 i-k)]=0

r \×(3 i+j-k)=0

Here

r=n(3 i+j-k)

There is only one option

(3 i+j-k)

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