Question

Two vectors 3i and 3j 3k what will be the resultant

Answer 1

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 = 0.574

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Faizan Ahmed

Jai Prakash Chauhan

Jai Prakash Chauhan, works at Udaipur, Rajasthan, India

Answered Aug 5

Resultant vector (R) = sum of both vectors

R = 8i + 7i + 9k

x axis is represented by x = 1i

Angle between R and x = cos# = R.x/Rx

cos# = (8x1 + 7x0 + 9x0)/ sqrt(8^2 + 7^2 + 9^2)(1)

cos# = 8/sqrt(64+49+81)

cos# = 8/sqrt(194)