Question

If P=2i + 4j + 3k and Q = i +5j - 2k, find P x Q

Answer 1

Answer:

P = 2i + 4j + 3k

Q = i + 5j - 2k

=> P x Q

=> i (4·(-2) - 3·5) - j (2·(-2) - 3·1) + k (2·5 - 4·1)

=> i (-8 - 15) - j (-4 - 3) + k (10 - 4)

=> -23i + 7j + 6k

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Answer 2

$\bf P\times Q = - 23 i + 7j +6 k$

Given:

• $P=2i + 4j + 3k \: \: and \: \: Q = i +5j - 2k$

To find:

• Find the cross product.

Solution:

Concept/formula to be used:

Cross product of two vectors is a vector quantity.

Let ,

$P=li + mj + nk \: \: and \: \: Q = xi +yj + zk$

then

$\bf P\times Q = \left| \begin{array}{ccc}i&j&k\\l&m&n\\x&y&z\end{array}\right|$

To find the cross product of the given vectors, P and Q, put the components of i,j and k in the determinant.

$P\times Q = \left| \begin{array}{ccc}i&j&k\\2&4&3\\1&5& - 2\end{array}\right|$

$= i( - 8 - 15) - j (- 4 - 3) + k(10 - 4)$

$= - 23 i + 7j +6 k$

Thus,

$\bf P\times Q = - 23 i + 7j +6 k$

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