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If a and b are two unit vectors such that angle between them is 60 , then |ab| =
1. 5
2. 3
3. 0
4. 1

Answer
VerifiedVerified
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Hint: To solve this question you must know the basic properties and formulas which we use in vectors now here since we know that the angle between the two vectors is 60 then we also know the cosine value between them which we can write as θ=60. Now since it is also said that these are unit vectors we can say that |a|=|b|=1. We can solve this question by the known formula that
|ab|=|a|2+|b|22|a|×|b|×cosθ

Complete step-by-step solution:
Now here since both of those vectors are unit vectors we can say that the magnitude of both of them will be equal to one. Now we let one vector to be a and other vector to be b. Therefore we can write the above expressed statement in a mathematical expression that
|a|=|b|=1
Now here it is also said that the angle between the two vectors is also 60 therefore we can write it in the form of cosine function so that we can substitute it in the formula we can write is as
θ=60
Now substituting all of these values we know in the formula for vector subtraction which is |ab|=|a|2+|b|22|a|×|b|×cosθ we get
|ab|=12+122×cos60
Putting the value for cosine we get
|ab|=12+122×12
Multiplying ;
|ab|=12+121
Taking the square and adding and subtracting
|ab|=1
Hence this is how we got the answer we needed. The answer for this question is option 4.

Note: A vector is a type of line that will always have magnitude and direction. The length of the line shows its magnitude and the arrowhead points in the direction. We can add two vectors by joining those head-to-tail. We can also subtract two vectors by first taking a negative of a vector, that is take the vector completely opposite it and then add it with the other vector.

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