Question

Let a=4i+5j-k, b=i-4j+5k and c=3i+j-k . Find a vector d which is perpendicular to both a and b and

d.A = 21.

Answer 1

Answer:

Step-by-step explanation:

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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Answer 2

Answer:

d = 21i - 21j - 21k

Step-by-step explanation:

a = 4i + 5j - k

b = i - 4j + 5k

c = 3i + j - k

To find a vector d that is perpendicular to both the vectors a and b can be find by finding the cross product of a and b

⇒ d = a × b

$\implies d=\begin{vmatrix}i & j & k\\ 4 & 5 & -1\\ 1 &-4& 5\end{vmatrix}\\\\\implies d=21i-21j-21k$