If the acceleration and velocity of a charged particle moving in a constnt magnetic region is given by `a=a_1hati+a_2hatk, v=b_1hati+b_2hatk.[a_1,a_2,b_1` and `b_2` are constant]. Then choose the wrong statement

If the points ( a_1,b_1),(a_2,b_2) and (a_1+a_2,b_1+b_2) are collinear ,show that a_1b_2=a_2b_1 .

If a=hati+hatj+hatk,a.b=1andaxxb=hatj-hatk then b=

Let the vectors veca,vecb,vecc be given as : a_1hati+a_2hatj+a_3hatk,b_1hati+b_2hatj+b_3hatk,c_1hati+c_2hatj+c_3hatk . Then show that vecaxx(vecb+vecc)=vecaxxvecb+vecaxxvecc .

Assertion: veca=hati+phatj+2hatk and hatb=2hati+3hatj+qhatk are parallel vectors if p=3/2, q=4 , Reason: If veca=a_1hati+a_2hatj+a_3hatk and vecb=b_1hati+b_2hatj+b_3hatk are parallel then a_1/b_1=a_2/b_2=a_3/b_3 . (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: veca=hati+phatj+2hatk and hatb=2hati+3hatj+qhatk are parallel vectors if p=3/2, q=4 , Reason: If veca=a_1hati+a_2hatj+a_3hatk and vecb=b_1hati+b_2hatj+b_3hatk are parallel then a_1/b_1=a_2/b_2=a_3/b_3 . (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If veca=a_1hati+a_2hatj and vecb=b_1 hati+b_2hatj are non zero vectors then prove that they are paralel if and only if a_1 b_2-a_2b_1=0

If veca=a_1hati+a_2hatj and vecb=b_1 hati+b_2hatj are non zero vectors then prove that they are paralel if and only if a_1 b_2-a_2b_1=0

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .