Calculate the angle between vectors i + j and i – j
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here is your and we should do dot product of the vactor
let A = I +j ,B = i - j
A .B = |A| . |B| cos @
A. B = (I + j) .(I - j )
= (I . I ) + ( j.I)- ( I.j ) - ( j.j )
I.I = | I| . |I| cos @
angle between both is zero
so cos0° = 1
similarly j.j = 1 and j.I and I.j is 0 becz both vector are perpendicular
do A.B = 1+ 0+ 0+1 = 2
so 2 = |A| |B| cos @
|A| = √ |1|^2+ |1|^2 + 0
= √ 2
similarly |B| = √2
2= √2 .√2cos@
2 = 2 cos @
cos@= 1
cos@= cos 0°
@ = 0°
let A = I +j ,B = i - j
A .B = |A| . |B| cos @
A. B = (I + j) .(I - j )
= (I . I ) + ( j.I)- ( I.j ) - ( j.j )
I.I = | I| . |I| cos @
angle between both is zero
so cos0° = 1
similarly j.j = 1 and j.I and I.j is 0 becz both vector are perpendicular
do A.B = 1+ 0+ 0+1 = 2
so 2 = |A| |B| cos @
|A| = √ |1|^2+ |1|^2 + 0
= √ 2
similarly |B| = √2
2= √2 .√2cos@
2 = 2 cos @
cos@= 1
cos@= cos 0°
@ = 0°
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