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Motion in Straight Line

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is,

  • 90o

  • 45o

  • 180o

  • 0o


A.

90o

There are two vectors P and Q.

It is given that,

open vertical bar straight P plus straight Q close vertical bar space equals open vertical bar P minus Q close vertical bar
Let, angle between P and Q is straight ϕ,
straight P squared plus straight Q squared space plus space 2 PQ space cosϕ space equals space straight P squared space plus space straight Q squared space minus space 2 space PQ space cos space straight ϕ
rightwards double arrow space 4 PQ space cos space straight ϕ space equals space 0

rightwards double arrow space cos space straight ϕ space equals space 0 space left square bracket because space straight P comma space straight Q space not equal to space 0 right square bracket

rightwards double arrow space straight ϕ space equals space straight pi over 2 equals space 90 to the power of straight o

There are two vectors P and Q.

It is given that,

open vertical bar straight P plus straight Q close vertical bar space equals open vertical bar P minus Q close vertical bar
Let, angle between P and Q is straight ϕ,
straight P squared plus straight Q squared space plus space 2 PQ space cosϕ space equals space straight P squared space plus space straight Q squared space minus space 2 space PQ space cos space straight ϕ
rightwards double arrow space 4 PQ space cos space straight ϕ space equals space 0

rightwards double arrow space cos space straight ϕ space equals space 0 space left square bracket because space straight P comma space straight Q space not equal to space 0 right square bracket

rightwards double arrow space straight ϕ space equals space straight pi over 2 equals space 90 to the power of straight o

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