If F 10 i 10 j 10 k N and G 20i 20j 20k N then F G N

If F= {10 i + 10 j + 10 k} N and G = {20i + 20j + 20k} N, then F + G= {} N 10i + 10 j + 10 k 30 i + 20 j + 30 k -10i - 10 j- 10 k 30 i + 30 j + 30 k Find the dot product of the two vectors P and Q, if P ={5 i +2 j + 3 k} m Q = {-2 i + 5 j + 4 k} m -12 m 12 m 12 m^2 -12 m^2 10 m^2 Resolve F along x and y axes and write it in vector form, then F={}N

Solution

6.

Here we need to add two vectors which is done by adding component wise ie component along i gets added to component along i and so on

So,

F+G=(10+20)i+(10+20)j+(10+20)k=30i+30j+30k

7. We need to take dot product here. Here we multiply the components and add the product

ie multiply ith component with ith component, jth with jth and kth with kth and add the products

So, P.Q= 5*(-2)+2*5+3*4=12

8

We are given angle F makes with negative y axis. Magnitude of F is given as 80 N

SO component of F along negative y axis is :80 cos(30)

HEnce component of F along y axis is :-80 cos(30)

Component of F along x axis is:80 sin(30)

So,

F=80 sin(30)i-80 cos(30)j

So option C