Question

If A= 5i+3j and B 2i+4j the direction of the resultant vector of their qddition is
1. 90
2. 45
3. 60
4. 120​

Answer 1

Answer:

If the resultant of the vectors 3i+4j+5k and 5i+3j+4k makes an angle # with an x-axis, then what is cos#?

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Let A=3i+4j+5k and B=5i+3j+4k

then the resultant C, can be written as

C=A+B=8i+7j+9k

As we know a unit vector along x-axis is i,

Hence the required angle # between C and i can be given as

Cos# = {C.i}/C.i [C and i are magnitudes of C and i , This relation comes from the dot product of vectors where A.B = AB.Cosθ → Cosθ =A.B/AB]

Now we need to know the components on RHS.

C = √(8²+7²+9²) =√(64+49+81) = √194 = 13.93

i = 1

C.i = (8i+7j+9k).i = 8+0+0 = 8

So now Cos# = {C.i}/C.i = 8/13.93=

120

So 4 is the correct answer