If d Subscript 1 Baseline Overscript right-arrow EndScripts plus d Subscript 2 B

Question

If d Subscript 1 Baseline Overscript right-arrow EndScripts plus d Subscript 2 Baseline Overscript right-arrow EndScripts equals 5.0 d Subscript 3 Baseline Overscript right-arrow EndScripts , d Subscript 1 Baseline Overscript right-arrow EndScripts minus d Subscript 2 Baseline Overscript right-arrow EndScripts equals 1.0 d Subscript 3 Baseline Overscript right-arrow EndScripts and d Overscript right-arrow EndScripts Subscript 3 Baseline equals 1.4 i Overscript ? EndScripts plus 4.6 j Overscript ? EndScripts , then what are (a) the x component of d Subscript 1 Baseline Overscript right-arrow EndScripts , (b) the y component of d Subscript 1 Baseline Overscript right-arrow EndScripts , (c) the x component of d Subscript 2 Baseline Overscript right-arrow EndScripts , and (d) the y component of d Subscript 2 Baseline Overscript right-arrow EndScripts ?

Explanation / Answer

SOLUTION:

Let vector d1 = d1x + d1y = d1 i + d1 j

and vector d2 = d2x + d2y = d2 i + d2 j

d3 = d3x + d3y = 1.4 i + 4.6 j

from givens, d1 + d2 = 0.5 d3 and d1 - d2 = 1.0 d3

=> (d1 i + d1 j) + ( d2i + d2j) = 0.5 (1.4 i +4.6 j)

and (d1 i + d1 j) - ( d2i + d2j) = 1.0 (1.4 i +4.6 j)

add these two equations

=>  [(d1 i + d1 j) + ( d2i + d2j) ] + [ (d1 i + d1 j) - ( d2i + d2j) ] = 0.5 (1.4 i +4.6 j) + 1 (1.4 i +4.6 j)

=> d1 i + d2 j = 1.5 (1.4 i +4.6 j)

=> vector d = 2.1 i + 6.9 j

now from the 1st equation,

d1x +d1y +(d2x+d2y) = 0.5 (1.4 i +4.6 j)

=> d2x+d2y = ( 0.7 i + 2.3 j ) -( 2.1 i + 6.9 j)

=> vector d2 = -1.4 i - 4.6 j

a) X component of d1 = 2.1 i

b) Y component of d1 = 6.9 j

c) X component of vector d2 = -1.4 i

d) Y component of d2 = -4.6 j

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