GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 15 of 65

Marks: +1, -0

For three vectors

{A}↖{→}=2 {j}↖{∧}-3 k ⋅ {B}↖{→}=-2 {i}↖{∧}+k

and

{C}↖{→}=3 {i}↖{∧}-{j}↖{∧}

, where

{i}↖{∧}, {j}↖{∧}

and

k

are unit vectors along the axes of a right-handed rectangular\/Cartesian coordinate system, the value of

({A}↖{→} ⋅({B}↖{→} × {C}↖{→})+6)

is_____________.

Solution:

{A}↖{→}=2 {j}↖{∧}-3 {k}↖{∧}, \;\; {B}↖{→}=-2 {i}↖{∧}+{k}↖{∧}

{C}↖{→}=3 {i}↖{∧}-{j}↖{∧}

{ {A}↖{→}({ {B}↖{→} × { {C}↖{→})

=|\table 0 , 2 , -3 ; -2 , 0 , 1 ; 3 , -1 , 0|

=-2(-3)-3(2)

=0

∴ { {A}↖{→}({ {B}↖{→} × { {C}↖{→})+6=6

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