Question

If P bar = 2i^+3j^-k^and Q=2i^-5j^+2k^find P ×Q.

Answer 1

Answer:

If P bar = 2i^+3j^-k^ and Q=2i^-5j^+2k^find P ×Q$=i-6j-16k$

Explanation:

A vector is a physical quantity that has both magnitude and direction

The cross product or vector product is one of the multiplications of vector algebra

If two vectors A and B are inclined to an angle $\alpha$, then the cross product is given by the formula $A$×$B$$=/A//B/sin\alpha$

for two vectors written in component form as

$A=a_{1} i+a_{2} j+a_{3} k$ and $B=b_{1} i+b_{2} j+b_{3} k$

the cross product

$A$× $B=(a_{2} b_{3} -a_{3} b_{2} )i-(a_{1} b_{3} -a_{3} b_{1} )j+(a_{1} b_{2} -a_{2} b_{1} )k$

From the question, we have two vectors

$P=2i+3j-k$ and $Q=2i-5j+2k$

substitute the given components to find the cross product of the two vectors

$P$×$Q=$ $(6-5)i-(4--2)j+(-10-6)k=i-6j-16k$