NIMCET 2023 Question Paper with solutions

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Question : 42 of 120

Marks: +1, -0

Let

{a}↖{\^}={i}↖{\^}-{k}↖{\^}, {b}↖{\^}=x {i}↖{\^}+{j}↖{\^}+(1-x) {k}↖{\^} \;\;

and

{c}↖{\^}=y {i}↖{\^}+x {j}↖{\^}+(1+x-y) {k}↖{\^}

, then

[{a}↖{\^} {b}↖{\^} {c}↖{\^}]

depends on:

Only $x$
Neither $x$ nor $y$
Both $x$ and $y$
Only $y$

Solution:

{|\table 1 , 0 , -1 ; x , 1 , 1-x ; y , x , 1+x-y|}

\;= \{(1+x-y)- (x-x^2) \} -0- \{x^2-y\}

\;=1+x-y-x+x^2-x^2+y

\;=1

Depends Neither on

x

nor,

y

.

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