<PRE><B>Question 762177</B>
find a vector d which is perpendicular to both A = 4i+5j-k and B = i-4j+5k and which satisfies the relation D.C = 21, where C = 3i+j+2k
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The vectors perpendicular are AxB and BxA (cross products)
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AxB:
|+i +j +k|
|+4 +5 -1|
|+1 -4 +5|
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P = i*(25-4) - j*(20+1) + k*(-16-5)
P = 21i - 21j - 21k
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Do you mean the dot product of D and C?  If so,
Find P.C:
= 21*3 - 21*1 + 21*2 = 63
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D = P*(21/63) = P/3
Multiply the coefficients of P by 1/3
D = 7i - 7j - 7k
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You can do the same for the other vector, BxA</PRE>