Let x→ be a vector in the plane containing vectorsa→=2i^−j^+k^  and  b→=i^+2j^−k^ . If the vectorx→  is perpendicular to 3i^+2j^−k^ and its projection on a→  is 1762, then the value ofx→2  is equal to

Given x¯  is a coplanar vector with a¯ and b¯Hence, x¯=λa¯+μb¯=λ2i−j+k+μi+2j−k=i2λ+μ+j−λ+2μ+kλ−μGiven x¯⋅a¯=03λ+8μ=0      ......1Given the projection of x¯  on a¯  is 1762we get 6l−μ=51              .....2Solving the above two equations λ=8,μ=-3Therefore, x¯ =13i-14j+11k,  hence sqaure of its magnitude is 486