Question

if a is equals to i + J + 2K and b is equals to -2 i + 3j - 4 k.....find |a×b|​

Answer 1

Explanation:

A = i+j +2k

B = -2i +3j -4k

A×B =

| i j k|

|1 1 2|

|-2 3 -4|

i(-4-6) -j(-4+4) +k(3+2)

-10i +5k

Magnitude of vector

So |a×b| => √(10)^2 +(5)^2

=> √125

=> 15

Answer 2

$\huge{\sf{===Answer===}}$

Given :-

$\large{\sf{\overrightarrow{A} \: = \: \hat{i} \: + \: \hat{j} \: + \: 2\hat{k}}}$

$\large{\sf{\overrightarrow{B} \: = \: -2\hat{i} \: + \: 3\hat{j} \: - \: 4\hat{k}}}$

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To find :-

|A × B|

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Solution :-

$\large{\sf{|A \: \times \: B|}}$

⤵⤵⤵

|i j k|

|1 1 2|

|-2 3 -4|

Then,

${\sf{[(1(-4) - 2(3))\hat{i}] \: + \: [2(-2) - 1(-4)\hat{j}] \: + \: [1(3) - 1(-2)\hat{k}]}}$

$\large{\sf{(-4 -6)\hat{i} \: + \: (-4+4)\hat{j} \: + \: (3+2)\hat{k}}}$

$\large{\implies}{\boxed{\boxed{\sf{-10\hat{i} \: + \: 0\hat{j} \: + \: 5\hat{k}}}}}$

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Magnitude

$\large{\sf{|A \: \times \: B| \: = \: \sqrt{(10)^{2} \: + \: (5)^{2}}}}$

$\large{\sf{|A \: \times \: B| \: = \: \sqrt{100\: + \: 25}}}$

$\large{\implies}{\boxed{\boxed{\sf{|A \: \times \: B| \: = \: \sqrt{125}}}}}$