If a vector of magnitude 2 units makes an angle 3 with 2 i , 4 with 3 j and an acute angle with 4 k , then what are the components of the vector?

Step-by-step solution

Let, a have (a₁, a₂, a₃ ) components array ll & a₁ i +a₂ j +a₃ k & | a |=2 array Also, It is given that a make angle with 3 with 2 i , 4 with 3 j and an acute angle with 4 k Then we have, aligned a 2 i & =| a ||2 i | 3 (a₁ i +a₂ j +a₃ k ) 2 i & =2.2 1 2 2 a₁ & =2 a₁=1 a 3 j & =| a ||3 j | 4 aligned and 3 a₂=2 3 1 2 a₂= 2 aligned a 4 k & =| a ||4 k | 4 a₃ & =2 4 aligned = a₃ 2 Now, | a |=2 array ll & a₁^2+a₂^2+a₃^2 =2 & a₁^2+a₂^2+a₃^2=4 array Put, a₁=1 and a₂= 2 (1)^2+( 2 )^2+a₃^2=4 a₃^2= 1 When, a₃=-1 then, =- 1 2