Mathematics : Vector Algebra

Let a, b and c be distinct non-negative numbers. If the vectors  

• the Geometric Mean of a and b

• the Arithmetic Mean of a and b

• equal to zero

• equal to zero

If  are non -coplanar vector λ is a real number then

• exactly one value of λ

• no value of λ

• exactly three values of λ

• exactly three values of λ

• only y

• only x

• both x and y

• both x and y

The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is 

• 2 : 1

• 

• 3:2

• 3:2

Let  be three non-zero vectors such that no two of these are collinear. If the vector  is collinear with is collinear with  (λ being some non-zero scalar) then  equals

• λ

• λ

• λ

• λ

A particle is acted upon by constant forces  which displace it from a point  The work done in standard units by the forces is given by 

• 40

• 30

• 25

• 25

• all values of λ

• all except one value of λ

• all except two values of λ

• all except two values of λ

Let  be such that  If the projection   is equal to that of  are perpendicular to each other then  equals

• 2

• 
• 
• 

Let  be non-zero vectors such that  If θ is the acute angle between the vectors  then sin θ equals

• 1/3

• 

• 2/3

• 2/3

Let $\overrightarrow{u}$ be a vector coplanar with the vectors a $\overrightarrow{a} = 2\hat{i} + 3\hat{j} -\hat{k} and \overrightarrow{b} = \hat{j} +\hat{k}.$ $if \overrightarrow{u} is perpendicular to \overrightarrow{a} and \overrightarrow{u}.\overrightarrow{b} = 24, then \left|\overrightarrow{u}\right| is equal to:$

• 84

• 336

• 315

• 256