Question

If r= 2i+j and r2= i- 2j +3k, what is the angle between R1 and R2?

Answer 1

Answer:

hello friend here ur answer

Step-by-step explanation:

r2-r1=i-2j+3k-(2i+j)

=-i-3j+3k

angle of R1 and R1=squrerootoft1+9+9

=squqreroot19

Answer 2

Answer:

The angle between the given vectors is 90°

Step-by-step explanation:

Given vectors are

$r _{1} = 2i + j \\ r _{2} =i - 2j + 3k$

We know that for any two vectors,A and B the angle between two vectors is given by the relation as follows

$Cos\theta=\frac{A.B}{|A.B|}$

Now substituting the given vectors in the above relation we get the angle.

$cos\theta=\frac{(2i+j).(i-2j+3k)}{ \sqrt{ {2}^{2} + {1}^{2} . \sqrt{ {1}^{2} + {2}^{2} + {3}^{2} } } }$

We know that dot product between two vectors is directly multiplication and addition of the coefficients of the unit vectors in all three directions.Hence the dot product of the above vectors becomes

$cos\theta=\frac{2 \times 1 - 1 \times 2 + 0 \times 3}{ \sqrt{ {2}^{2} + {1}^{2} }. \sqrt{ {1}^{2} + {2}^{2} + {3}^{2} } } \\ = 0 \\ = > \theta = cos {}^{ - 1} (0) = \frac{\pi}{2} = 90 {}^{0}$

Hence,the angle between two vectors us found to be 90°

Therefore,The angle between the vectors r1 and r2 is 90°

#SPJ2