Arrange the vector subtractions so that their magnitudes are in decreasing order- If the two vectors A- and B- such that -A-B- acting at angle -a 60 o b 90 o c 180 od 120 o

The correct option is C c, d, b, a #160;Let, S⃗=A⃗ B⃗ So, S⃗.S⃗=(A⃗ B⃗).(A⃗ B⃗) For a): #160; |S⃗|^2=|A⃗|^2+|B⃗|^2 2|A⃗||B⃗|cos60^o=|A⃗|^2+ ...

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Standard XII

Mathematics

Special Integrals - 1

Arrange the v...

Question

Arrange the vector subtractions so that their magnitudes are in decreasing order. If the two vectors $\to A$ and $\to B$ such that $[| \to A | > | \to B |]$ acting at angle :
a) 60 $^{o}$
b) 90 $^{o}$
c) 180 $^{o}$
d) 120 $^{o}$

d, c, b, a

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a, b, d, c

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c, d, b, a

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c, d, a, b

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Solution

The correct option is C c, d, b, a
Let, $\to S = \to A - \to B$
So, $\to S . \to S = (\to A - \to B) . (\to A - \to B)$
For a): $| \to S |^{2} = | \to A |^{2} + | \to B |^{2} - 2 | \to A | | \to B | cos 60^{o} = | \to A |^{2} + | \to B |^{2} - | \to A | | \to B |$
For b) : $| \to S |^{2} = | \to A |^{2} + | \to B |^{2} - 2 | \to A | | \to B | cos 90^{o} = | \to A |^{2} + | \to B |^{2}$
For c) : $| \to S |^{2} = | \to A |^{2} + | \to B |^{2} - 2 | \to A | | \to B | cos 180^{o} = | \to A |^{2} + | \to B |^{2} + 2 | \to A | | \to B |$
For d) : $| \to S |^{2} = | \to A |^{2} + | \to B |^{2} - 2 | \to A | | \to B | cos 120^{o} = | \to A |^{2} + | \to B |^{2} + | \to A | | \to B |$
Thus, the descending order : $c > d > b > a$

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Arrange the vector subtractions so that their magnitudes are in decreasing order. If the two vectors →A and →B such that [|→A|>|→B|] acting at angle :a) 60o b) 90o c) 180od) 120o

Arrange the vector subtractions so that their magnitudes are in decreasing order. If the two vectors $\to A$ and $\to B$ such that $[| \to A | > | \to B |]$ acting at angle :
a) 60 $^{o}$
b) 90 $^{o}$
c) 180 $^{o}$
d) 120 $^{o}$