Vector (A+B) will be perpendicular to?
I had this question in my coaching test. Shouldn't Vector (A+B) be perpendicular to A-B as A=B? As they form a rhombus and the diagonals of a rhombus are perpendicular to each other. I also drew it and am getting them to be perpendicular, for both A-B and 3A-3B. I checked the answer on Byju's and Toppr but it is also marked as A cross B there, so something must be wrong with my solution.
30 Replies
@Gyro Gearloose
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.Firstly for any vector to be perpendicular to the other, it should lie in a different plane and have 90 degrees . In option B and C, the resultant vector lies in the same plane as A+B, thus it is not perpendicular
So î and j are not perpendicular huh?
but all of these is correct
Yes
Two vectors in different planes would always be perpendicular, but two vectors in the same plane could also be perpendicular when there is a right angle between them, right?
. product seems simple enough to explain this
Well yes, but in this case |A| = |B|, thus the only possibility of your statement wont work
Yes you are correct...i think question has misprint and it want you to ask that which of the following is perpendicular to A and B not A+B
but guys i think he is right for the question he got don't you agree?
46% people who attempted the test marked Option A and got it right
I get it, my bad
NVM 🙂
Taking a random case, consider two vectors with equal magnitude, vector A to be 3i+4j and vector B to be 4i+3j. (Both have a magnitude of 5 units). A+B would be equal to 7i+7j. A-B would be -1i+1j. The formula for dot product is a.b=abcosP where P is angle between a and b, so cos P = a.b/ab
(a+b).(a-b)=-7+7=0
ab = (root 98)(root 2)
so cos P = 0/(root 98)(root 2)=0, thus P = 90deg
It's working if I take a random case, but solution videos from PW and Doubtnut insist that A is the answer
in that case the question isnt clear they shouldve said perpendicular to the plane
Is it solved?
A-b is not always perpendicular to A + b
For example taking a and b to be in opposite directions like one goes north and one goes south ... in this case a-b is not perpendicular to a + b
@Takt
Ya but here magnitude of both is same
yes
so they wont be perpendicular right
I answered d for the same question , we both are part of the same coaching .
Bro they will pe perpendicular just do dot product and see
The dot product will be zero
yes , but why is it that in most of these websites the answer is a 😭
They might be wrong bro like meri jee mains ki shift me ek NLM ka question aaya jisme most sites ne ROD or contact point pe reaction force surface ke perpendicular nahi liya just to match the wrong answer of NTA
Thanks for this, I'll ask my physics teacher next class
Ok ask maths teacher too he may also help
He said we are right about this
+solved
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+solved @user. This will be added to their stats.+solved @Priyam Alok
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