Please kindly provide me the detailed solution Q5 â ‹Q5 If a→ = a, then find the - Maths - Vector Algebra

Question

Please kindly provide me the detailed solution Q5

â€‹Q5 If a → = a, then find the value of the
following :
a → × i ^ 2   +   a → × j ^ 2
  + a → × k ^ 2

Aarushi Mishra · Accepted Answer

Given: a→=aLet a→=x i^+y j^+z k^a→=x2+y2+z2=ax2+y2+z2=a2Nowa→×i^2+a→×j^2+a→×k^2=x i^+y j^+z k^×i^2+x i^+y j^+z k^×j^2+x i^+y j^+z k^×k^2=x i^×i^+y j^×i^+z k^×i^2+x i^×j^+y j^×j^+z k^×j^2+x i^×k^+y j^×k^+z k^×k^2=0+y -k^+z j^2+x k^+0+z -i^2+x -j^+y i^+02=0+y -k^+z j^2+x k^+0+z -i^2+x -j^+y i^+02=-y k^+z j^2+x k^-z i^2+-x j^+y i^2=y2+z22+x2+z22+x2+y22=y2+z2+x2+z2+x2+y2=2x2+y2+z2=2a2

Please kindly provide me the detailed solution. Q5 ​Q5. If a → = a, then find the value of the following : a → × i ^ 2 + a → × j ^ 2 + a → × k ^ 2

Please kindly provide me the detailed solution. Q5

Q5. If $|\vec{a}|$ = a, then find the value of the following :
${|\vec{a} \times \hat{i}|}^{2} + {|\vec{a} \times \hat{j}|}^{2} + {|\vec{a} \times \hat{k}|}^{2}$