NIMCET 2023 Question Paper with solutions

Question : 15 of 120

Marks: +1, -0

If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is:

$\;{15}/{3}$ unit
$5 {√{3}}$ unit
$\;{15 {√{3}}}/{2}$ unit
None of these

Validate

Solution:

|{v}↖{→}|=5

{v}↖{→}

makes equal angle with all the three axis

{v}↖{→}\;=x {i}↖{\^}+x {j}↖{\^}+x {k}↖{\^}

|{v}↖{→}|\;={√{3}} x=5

x\;=\;{5}/{{√{3}}}

Sum of component on

x, y, z

axis

x+x+x=3 (\;{5}/{{√{3}}}) =5 {√{3}} .

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