Question

1.Determine the value of a so that vector 𝑨⃗⃗ =(𝟏𝟎𝒊̂+𝟏𝟒𝒋̂−𝟔𝒌̂) is perpendicular to vector 𝑨⃗⃗ =(𝟏/𝟐𝒊̂+𝟏/𝟐𝒋̂+𝒂𝒌̂)

2. A particle covers a distance of (𝟐𝒊̂+𝟑𝒋̂+𝟓𝒌̂) metres in the direction of a constant force of (𝟕𝒊̂+𝟖𝒋̂+𝟑𝒌̂) newtons acting on it. Calculate the work done by the force on this particle.

3. A body moves from position (𝟐𝒊̂+𝟐𝟎𝒋̂−𝟏𝟖𝒌̂) metres to a position

(𝟏𝟔𝒊̂+𝟐𝟒𝒋̂+𝟏𝟓𝒌̂) metres when a force of (𝟒𝒊̂+𝟐𝒋̂+𝟑𝒌̂) newton is applied on it. Calculate the work done on a body.

4. A point of application of a force 𝑭⃗⃗ =(𝟏𝟔𝒊̂+𝟐𝟎𝒋̂+𝟏𝟓𝒌̂) is moved from

𝒓𝟏⃗⃗⃗⃗ =(𝟐𝒊̂+𝟕𝒋̂+𝟐𝒌̂) to 𝒓𝟐⃗⃗⃗⃗ =(𝟓𝒊̂+𝟏𝟐𝒋̂+𝟑𝒌̂). Find the work done.

Answer 1

1)

$$(10,14,-6)\cdot(0.5,0.5,a)=5+7-6a=0\\a=2$$

2)

$$W=Fr=(2,3,5)\cdot(7,8,3)\\=14+24+15=53\ J$$

3)

$$\Delta r=(16,24,15)-(2,20,-18)=(14,4,33)\ m$$

$$W=F\Delta r=(4,2,3)\cdot(14,4,33)=163\ J$$

4)

$$\Delta r=(5,12,3)-(2,7,2)=(3,5,1)\ m$$

$$W=F\Delta r=(16,20,15)\cdot(3,5,1)=163\ J$$