Question

I am confused with the following 3 vector questions ( from competitive exams ) [ plz note that I have written vectorA,B,C as I am not able to put the vector sign on top of the alphabets )

1) Three vectors satisfy the relation vectorA.vectorB=0(zero) and vectorA.vectorC=0 . Then vectorA is parallel to a)vectorB.vectorC b)vectorB x vectorC

2) If vectorA x vectorB = vectorB x vectorA , then the angle b/w vectorA and vectorB is a)90 b)0

3)If the angle between the vectors A and B is theta , the value of the product (vectorB x vectorA).vectorA is equal to a)zero b)BA^2costheta

Plz guide

Answer 1

for first question..

when the dot product of two vectors is zero.. what can u say about the angle between the two vectors?


for second question

Remember A X B and B X A . will ALWAYS HAVE same magnitude and ALWAYS in opposite direction.. So A X B = - B X A


for third question there are couple of ways to think about it ( i like to do it pure mathematical reasoning)..
have u worked with box products (scalar tipple products) ?

Answer 2

Thanks a lot @Mashy ! . Clearly understood !
But for the 3rd ques , I have not learnt Scalar triple products . Plz explain it to me using any gud method ! Thanks

Answer 3

ok..

B X A = a vector PERPENDICULAR TO BOTH A and B (lets call this vector as C)

now what would happen if you dotted C with A ?

Answer 4

I think , it is parallel ! Am i right ? @Marshy

Answer 5

read what i wrote again :P.. and its @mashy

Answer 6

not able to get the ans !

Answer 7

A X B = C

C is perpendicular to BOTH A AND B

now if you do A dot C ( remember A is perpendicular to C) what happens? :P