A =a1i+a2j+a3k B=b1i +b2j+b3k where |a|=1 and |b|=4 a.b=2 The c=2(a x b) -3b Then find angle between b and c vector
Question
A = a1i + a2j + a3k
B = b1i + b2j + b3k
where |a|=1 and |b|=4
a.b=2
The c=2(a x b) -3b
Then find angle between b and c vector
Solution
To find the angle between vectors b and c, we can use the formula for the dot product of two vectors:
b.c = |b| |c| cos θ
where θ is the angle between the vectors, |b| is the magnitude of vector b, |c| is the magnitude of vector c, and b.c is the dot product of vectors b and c.
First, we need to find the vector c and its magnitude. Given that c = 2(a x b) - 3b, we can substitute the given vectors a and b into this equation to find c.
Next, we find the dot product of vectors b and c.
Finally, we substitute these values into the formula for the dot product of two vectors and solve for θ.
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