Let `veca=a_1hati+a_2hatj+a_3hatk, vecb=b_1hati+b_2hatj+b_3hatk and vecc=c_1hati+c_2hatj+c_3hatk` then show that `vecaxx(vecb+vecc)=vecaxxb+vecaxxvecc`

Let veca = a_1hati + a_2hatj + a_3hatk, vecb = b_1hati + b_2hatj+ b_3hatk and vecc = c_1hati + c_2hatj + c_3hatk be three non zero vectors such that |vecc| =1 angle between veca and vecb is pi/4 and vecc is perpendicular to veca and vecb then |[a_1, b_1, c_1], [a_2, b_2, c_2], [a_3, b_3, c_3]|^2= lamda(a_1 ^2 +a_2 ^2 + a_3 ^2)(b_1 ^2 + b_2^2+b_3^2) where lamda is equal to (A) 1/2 (B) 1/4 (C) 1 (D) 2

If veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb= b_(1)hati+b_(2)hatj + b_(3)hatk, vecc=c_(1)hati+c_(2)hatj+c_(3)hatk and [3veca+vecb 3vecb+vecc 3vecc + veca] =lambda|{:(veca.hati,veca.hatj,veca.hatk),(vecb.hati,veca.hatj,hatb.hatk),(vecc.hati,vecc.hatj,vecc.hatk):}| " then find the value of " lambda/4

if veca=hati-hatj-3hatk, vecb=4hati-3hatj+hatk and vecc=2hati+hatj+2hatk, verify that vecaxx(vecb+vecc)=vecaxxvecb+vecaxxvecc

If veca=2hati+2hatj-hatk, vecb=3hati-hatj-hatk and vecc=hati+2hatj-3hatk then verify that vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc .

If veca=7hati+3hatj-5hatk, vecb=2hati+5hatj-hatk and vecc-hati+2hatj+4hatk, then verify that vecaxx(b+c)=vecaxxvecb+vecaxxvecc

If veca=2hati+5hatj-7hatk, vecb=-3hati+4hatj+hatk and vecc=hati-2hatj-3hatk , show that ((vecaxxvecb)xxvecc), vecaxx(vecbxxvecc) are not same .

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb=b_(1)hati+b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk be three non zero vectors such that vecc is a unit vector perpendicular to both veca and vecb . If the angle between veca and vecb is (pi)/6 , then |(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|^(2) is equal to

If vecaa=hati+2hatj+3hatk, vecb=2hati-hatj+hatk and vecc=hati+hatj-2hatk, verify that vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc.

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=hati+hatj+hatk , vecb=2hati+hatj-hatk and vecc=4hati+3hatj+hatk then value of ((veca+vecb)xx(veca -(veca-vecb)xxvecb)))xxvecc is