IIT JEE , AIEEE Forum - Mathematics , Vectors

rohitkuruvila

A.(A*B)=?,A*B means A cross B,A and B are vectors

OPTIONS ARE

a)0

b)1

c)undefined equality

d)|A| |B|

siddharthsaxena

is it 0

rohitkuruvila

i had this question in a test.even i marked zero,but the answer key mentioned the answer of this question to be 1

rohitkuruvila

i took A=i^,B=j^

A.(A*B)=i^.(i^ * j^)

=i^.k^(since i^ * j^=k)

=0

is there something wrong with the way i did it

raghulmz

A.(A*B) is the box product of [A A B] expanding it into its matrix form we will get 2 identical rows hence A.(A*B) is zero.

also geometrically if 3 vectors lie in the same plane their box product is zero . A,A, B lie in the same plane (A and B lie in the same plane Because any 2 vectors lie in the same plane) so A.(A*B) is zero

neeraj_agarwal_1990

Its a result...
If two of the vectors are same while calculating scalar triple product,the answer is 0

answer is 0 even when two of the vectors are collinear or all 3 vectors are coplanar.....

(thats because the vol. of parallelopoid becomes 0...)

kane

let me tell you all something that in the question it is necessary to give direction of the vectors also.if both the vectors are having tha same drection then their cross-product is always zero.actually the answer is d because in this case

A X B= A B Sine of the angle b/w A & B which is 90* as i^{^} j^ k^ are perpendi cular to each other.

IAI X IBI i.e. magnitude of A & B vector resp.

plzzz rate me if i cleared your confusion

Akshay

A*B =R Now R and A are mutually perpendicular so.cos90=0.

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