Question

let A=i+j and B=2i-j. Magnitude of a copalner vector C such that A.C=BC=AB is given by​

Answer 1

The magnitude of coplanar vector C is √5/3

Explanation:

Given:

$\vec A=\hat i+\hat j$

$\vec B=2\hat i-\hat j$

To find out:

A coplanar vector $\vec C$

Such that

$\vec A.\vec C=\vec B.\vec C=\vec A.\vec B$

Solution:

Let the vector C be

$\vec C=x\hat i+y\hat j$

$\vec A.\vec B=(\hat i+\hat j).(2\hat i-\hat j)=2-1=1$

Thus,

$\vec A.\vec C=\vec B.\vec C=1$

$\vec A.\vec C=(\hat i+\hat j).(x\hat i+y\hat j)$

$\implies x+y=1$

Similarly

$\vec B.\vec C=(2\hat i-\hat j).(x\hat i+y\hat j)$

$\implies 2x-y=1$

Adding both the equations

$3x=2$

$\implies x=\frac{2}{3}$

Therefore,

$y=1-x=1-\frac{2}{3}=\frac{1}{3}$

Thus, the vector $\vec C$ is

$\vec C=\frac{2\hat i+\hat j}{3}$

The magnitude of $\vec C$ is

$|\vec C|=\frac{1}{3}(\sqrt{2^2+1^2})$

$\implies |\vec C|=\frac{\sqrt{5}}{3}$

Hope this answer is helpful.

Know More:

Q: Given three coplanar vector a=4i-j,b=-3i+2j and c=-3j.find the magnitude of the sum of the three vectors.

Click Here: https://brainly.in/question/5664379

Q: Three vectors a,b and c satisfy the relation a.b=0 and a.c=0. The vector a is parallel to:

Click Here: https://brainly.in/question/7917978

Answer 2

there is no problem to this question so surely correct this question