Unit Vectors

Since

%5Cmathbf%7Ba%7D

and

%5Cmathbf%7Bb%7D

are unit vectors and the angle between them is

%5Cfrac%7B%5Cpi%7D%7B3%7D

, we know that:

%5Cmathbf%7Ba%7D%20%5Ccdot%20%5Cmathbf%7Bb%7D%20%3D%20%5Ccos%5Cleft(%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright)%20%3D%20%5Cfrac%7B1%7D%7B2%7D.

For the vectors

%5Clambda%20%5Cmathbf%7Ba%7D%20%2B%202%20%5Cmathbf%7Bb%7D

and

3%20%5Cmathbf%7Ba%7D%20-%20%5Clambda%20%5Cmathbf%7Bb%7D

to be perpendicular, their dot product must be zero:

(%5Clambda%20%5Cmathbf%7Ba%7D%20%2B%202%20%5Cmathbf%7Bb%7D)%20%5Ccdot%20(3%20%5Cmathbf%7Ba%7D%20-%20%5Clambda%20%5Cmathbf%7Bb%7D)%20%3D%200.

Expanding this:

%5Clambda%20%5Ccdot%203%20%2B%202%20%5Ccdot%20(-%5Clambda)%20%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%20%3D%200.

Solving this gives

%5Clambda%20%3D%200

. Therefore, there is only 1 value of

%5Clambda

Chapter Questions
1 MCQs