Find the cross product of two vectors A - 3 - - 2 - - 4 k- and B- - 2 - - 3 - - 6 k- Also find the magnitude of A-B-

Cross product of two vectors,Hwew #160; A⃗=3î+2ĵ 4k̂ a_1=3 a_2=2 a_3= 4 B⃗=2î 3ĵ 6k̂ b_1=2 b_2= 3 b_3= 6 is given by: A⃗×B⃗ =î #160; amp ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Find the cros...

Question

Find the cross product of two vectors $¯ ¯¯ ¯ A = 3^i + 2^j - 4^k$ and $\to B = 2^i - 3^j - 6^k$ . Also find the magnitude of $\to A \times \to B$

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Solution

Cross product of two vectors,
Hwew
$\to A = 3^i + 2^j - 4^k a_{1} = 3 a_{2} = 2 a_{3} = - 4$
$\to B = 2^i - 3^j - 6^k b_{1} = 2 b_{2} = - 3 b_{3} = - 6$
is given by:
$\to A \times \to B = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} \end{matrix} ∣ ∣ ∣ ∣ ∣ =^i (a_{2} b_{3} - b_{2} a_{3}) -^j (a_{1} b_{3} - b_{1} a_{3}) +^k (a_{1} b_{2} - b_{1} a_{2})$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 3 & 2 & - 4 2 & - 3 & - 6 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$=^i [(2 x - 6) - (- 3 x - 4)] -^j [(3 x - 6) - (2 x - 4)] + -^k [(3 x - 3) - (2 x 2)]$
$^i (- 12 + 12) -^j (- 18 + 8) +^k (- 9 - 4)$
$\to A \times \to B = - 24^i + 10^j - 13^k$
For magnitude,
$| \to A \times \to B | = \sqrt{a^{2} + b^{2} + c^{2}}$
$= \sqrt{(- 24)^{2} + (10)^{2} + (- 13)^{2}}$
$= \sqrt{845}$
$| \to A \times \to B | = 29.06 u n i t s$

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Find the cross product of two vectors ¯¯¯¯A=3^i+2^j−4^k and →B=2^i−3^j−6^k. Also find the magnitude of →A×→B

Find the cross product of two vectors $¯ ¯¯ ¯ A = 3^i + 2^j - 4^k$ and $\to B = 2^i - 3^j - 6^k$ . Also find the magnitude of $\to A \times \to B$