Operations on vectors

After finding the projection of vector u; u=〈3,2〉, onto vector v; v=〈5,-5〉, find w₂.

• 〈5/2,5/2〉

• 〈-5/2,5/2〉

• 〈5/2,-5/2〉

• 〈-5/2,-5/2〉

The diagram shows a rhombus, spanned by two vectors a and b .

Which of the following must be true?

• 
• 
• 
• 

• 7

• 6

• 5

• 4

• 3

• 58°

• 72°

• 74°

• 87°

What is the angle between two orthogonal vectors?

• 180 degree

• Pi/2

• Pi/ 4

• 45 degree

The points P , Q and R are collinear. It is given that

PQ = 3p + 2q and QR = ( 1-k )p + 4q where k is a constant. Find the value of k.

• k=5

• k=3

• k=-3

• k=-5

P, Q and R are three points in space where $\overrightarrow{PQ}\ =<2,2,-1>$   and  $\overrightarrow{PR}=<1,2,2>$   . 
Find the area of the triangle PQR.          

• 5.53  $unit^2$  

• 3.04  $unit^2$  

• 3.55  $unit^2$  

• 4.03  $unit^2$  

Given that a = 2i - 4j, b = 3i - 4j, and c = 11i + kj. If a + 3b is parallel to c, find the value of k.

• -16

• 11

• 16

• -11

• -1