Question

Let  be a unit vector and  a non-zero vector not parallel to . The angles of the triangle, two of whose sides are represented by  

Solution

Correct option is

π/6, π/3, π/2

 

We have,   

         

Thus, two sides of the triangle are represented by the vectors  

        

Since  is perpendicular to . Therefore, angle between the sides represented by the given vectors is a right angle.  

Now,   

        

  

  

Thus, the lengths of the sides containing the right angle of the triangle are in the ratio . So, the other two angles are π/6 and π/3.

SIMILAR QUESTIONS

Q1

Which of the following expressions are meaningful?

Q2

For three vectors  which of the following expressions is not equal to any of the remaining three?

Q3

 are linearly dependent vectors and , then

Q4

The volume of the tetrahedron whose vertices are the points with position vectors  and  is 11 cubic units if the value of λ is 

Q5

If a vector  is expressed as the sum of two vectors  along and perpendicular to a given vector 

Q6

 are two given vectors. On these vectors as adjacent sides a parallelogram is constructed. The vector which is the altitude of the parallelogram and which is perpendicular to  is not equal to

Q7

Three vectors  taken two at a time form three planes. The three unit vectors drawn perpendicular to three planes form a parallelopiped of volume  

Q8

 If  is a vector such that  and the angle between  is 30o, then  

Q9

Let  be two non-collinear unit vectors. If 

Q10

If the vectors  are coplanar, then the value of pqr – (p + q + r) is