Concept of Scalar Product

If the dot product of two vectors is equal to zero, then what do we know about the two vectors?

• They are parallel.

• They are orthogonal.

• They are neither.

The scalar product can be used to find the angle between two vectors

• True

• False

State the property of scalar product.

• A · B = B · A.

• A.(B+C) = (A+B) . (A+C)

• (3A) . B = - 3 . (AB)

Find the dot product of <1, -2> and <3, 2>.

• 1
• <3, -4>
• <4, 0>
• -1

Find the dot product of u and v if u = <7, 4> and v = <2, -3>.

• 8

• <14, -12>

• 2

• <9,1>

If $\overrightarrow{\ \ a}=3i\ +5j+k\ \ and\ \overrightarrow{\ \ b}=2i+j+3k\ then\ \overrightarrow{\ \ a}\ .\overrightarrow{\ \ b}=$  

• 41

• 12

• 21

• 14

Given  $a=2i+3j+4k$  
              $b=-i-2j-3k$  
Find  $a\cdot b$  

•  $-18$  

•  $-20$  

•  $20$  

Given  $a=2i+3j+4k$  
              $b=-i-2j-3k$  
Find  $\theta$  

•  $173.02\degree$  

•  $6.98\degree$  

•  $16.48\degree$  

If   $u\ \cdot v\ =\ 0$ , then  $u\ =\ 0\$  and  $v\ =\ 0$ . 

• True 

• False

How do you know if two vectors are orthogonal?

• Their sum is 0.
• The dot product is 1.
• The angle between them is 0°.
• The dot product is 0.