If R-P-Q- -show that P-R-P-Q-

Consider the equation #10; #10; R⃗=P⃗+Q⃗ #10; #10;Taking the cross product of above equation with P⃗ #10; #10; (P⃗×R⃗)=P⃗× (P⃗+Q⃗) ...

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Multiplication with Vectors

If R⃗=P⃗+Q⃗...

Question

If $\to R = \to P + \to Q$ ,show that $(\to P \times \to R) = (\to P \times \to Q)$ .

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Solution

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[\to p + 2 \to q + 3 \to r \to q + 2 \to r + 3 \to p \to r + 2 \to p + 3 \to q] = 54

\to p

\to q

\to r

∣ ∣ ∣ ∣ \begin{matrix} \to p . \to p & \to p . \to q & \to p . \to r \to p . \to q & \to q . \to q & \to q . \to r \to p . \to r & \to r . \to q & \to r . \to r \end{matrix} ∣ ∣ ∣ ∣

\to P

\to Q

\to R

| \to P |

= | \to Q |

| \to R |

= \sqrt{2}

| \to P |

\to P + \to Q

+ \to R = 0

\to P

\to Q

\to Q

\to R

\to P

\to R

\to q, \to r

\to p = \to q \times \to p + \to r

\to p = (2, - 10, 2)

\to q = (3, 1, 2)

\to r = (2, 1, 3)

| \to p \times (\to q \times \to r) | =

\to p, \to q, \to r

\to x

\to p \times ((\to x - \to q) \times \to p) + \to q \times ((\to x - \to r) \times \to q) + \to r \times ((\to x - \to p) \times \to r) = 0

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