Question

The force 8 = (î+bị+3ậ)N is rotated through an angle a , then it becomes (2î +(2b - 1)j + kN. The value of b is :-​

Answer 1

Answer:

2 or -2/3

Explanation:

According to the question,by rotating vector the vector will remain same.

Therefore we will equate the magnitude of the two vectors.

√1²+b²+3²=√2²+(2b-1)I+1²

Or,1+b²+9=4+(2b-1)I+1[squaring both sides]

Or,b²+10=5+4b²+1-4b

Or,3b²-4b-4=0

Factorizing by discriminant method:

b=-(-4)+√(-4)²-4*3*-4/2*3

b=4+√16+48/6=4+8/6

Or b=2

For negative value of b:

b=4-√16+48/6

=-2/3

Therefore,b has two values.b=

2 or -2/3

Answer 2

Answer:

b=  2 or -2/3

Explanation:

According to the question, by rotating vector the vector will remain same.

Therefore we will equate the magnitude of the two vectors.  

√1²+b²+3²=√2²+(2b-1)I+1²  

Or,1+b²+9=4+(2b-1)I+1[squaring both sides]  

Or,b²+10=5+4b²+1-4b  

Or,3b²-4b-4=0  

Factorizing by discriminant method:

b=-(-4)+√(-4)²-4*3*-4/2*3  

b=4+√16+48/6=4+8/6  

Or b=2  

For negative value of b:  

b=4-√16+48/6  

=-2/3  

Therefore,b has two values.b=  

2 or -2/3

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