Question

If a vector is equal to 2i vector + j vector + 3 k vector and b vector is equal to 3 I vector + 5 j vector - 2K vector then find the value of A vector into B vector​

Answer 1

Explanation:

[ i^ j^ k^ ] A vector × B vector = [ 2 1 3 ]

[ 3 5 -2 ]

= i^ (-2-15) - j^(-4-9) + k^(10-3)

= -17i^ + 13j^ + 7k^

Answer 2

$\huge \fcolorbox{red}{pink}{Solution :)}$

Given ,

$\sf \star \: \: A = 2 \hat{i}+ \hat{J} +3 \hat{k} \\ \star \: \: \sf</p><p>B = 3 \hat{i}+ 5 \hat{j}-2 \hat{k}$

Now , the cross product of two vectors A and B is

$\sf \hookrightarrow \vec{A} \times \vec{B} = (2 \hat{i}+ \hat{J} +3 \hat{k}) \times ( 3 \hat{i}+ 5 \hat{j}-2 \hat{k}) \\ \\ \sf \hookrightarrow \vec{A} \times \vec{B} = \hat{i} \bigg( 1 \times ( - 2) - 5 \times 3 \bigg) - \hat{j} \bigg(2 \times ( - 2) - 3 \times 3 \bigg) + \hat{k} \bigg(2 \times 5 - 3 \times1 \bigg) \\ \\ \sf \hookrightarrow \vec{A} \times \vec{B} = \hat{i}( - 2 - 15) - \hat{j}( - 4 - 9) + \hat{k}(10 - 3) \\ \\ \sf \hookrightarrow \vec{A} \times \vec{B} =\hat{i}( - 17) - \hat{j}( -13) + \hat{k}(7) \\ \\ \sf \hookrightarrow \vec{A} \times \vec{B} = - 17 \hat{i} + 13 \hat{j} + 7 \hat{k}$

Hence , the cross product of Vectors A and B is -17i + 13j + 7k

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