Determine A - B if A-x1-y1-z1k- B-x2-y2-z2k-

Given that, #10; #10; #160; #10;A⃗=x_1î+y_1ĵ+z_1k̂ #10; #10; #160; #10;B⃗=x_2î+y_2ĵ+z_2k̂ #10; #10;Now, cross product of A⃗ a ...

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Standard XII

Physics

Multiplication with Vectors

Determine A...

Question

Determine $A \times B$ if
$\to A = x_{1}^i + y_{1}^j + z_{1}^k$
$\to B = x_{2}^i + y_{2}^j + z_{2}^k$

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Solution

Given that,

$\to A = x_{1}^i + y_{1}^j + z_{1}^k$

$\to B = x_{2}^i + y_{2}^j + z_{2}^k$

Now, cross product of $\to A$ and $\to B$

$\to A \times \to B = (x_{1}^i + y_{1}^j + z_{1}^k) \times (x_{2}^i + y_{2}^j + z_{2}^k)$

$\to A \times \to B =^i (z_{2} y_{1} - y_{2} z_{1}) -^j (z_{2} x_{1} - x_{2} z_{1}) +^k (y_{2} x_{1} - x_{2} y_{1})$

Hence, this is the required solution

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Determine A×B if →A=x1^i+y1^j+z1^k →B=x2^i+y2^j+z2^k

Given that, →A=x1^i+y1^j+z1^k →B=x2^i+y2^j+z2^k Now, cross product of →A and →B →A×→B=(x1^i+y1^j+z1^k)×(x2^i+y2^j+z2^k) →A×→B=^i(z2y1−y2z1)−^j(z2x1−x2z1)+^k(y2x1−x2y1) Hence, this is the required solution

Determine $A \times B$ if
$\to A = x_{1}^i + y_{1}^j + z_{1}^k$
$\to B = x_{2}^i + y_{2}^j + z_{2}^k$