If a - 2i - 2j - 3k- b - 3 i- 2j - 4k are two vectors then dot product of vectors a and b will be - Maths Q-A

Find the dot product.We are given two vectors aand b as,a = 2î 2ĵ + 3k̂ ,0ex0exb = 3 î 2ĵ + 4k̂For vectors,a = a_1î + a_2ĵ + a_3k̂ ,0ex0exb = b_1î+ b_2ĵ + b_ ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

If a = 2i - 2...

Question

If $\vec{a} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are two vectors then the dot product of vectors $a$ and $b$ will be

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Solution

Find the dot product.
We are given two vectors $a$ and $b$ as,
$\vec{a} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k}$
For vectors,
$\vec{a} = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}, \vec{b} = b_{1} \hat{i} + b_{2} \hat{j} + b_{3} \hat{k}$
The dot product is given as, $a . b = a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}$
For the given two vectors, we have
$a . b = (2 \times 3) + (- 2 \times - 2) + (3 \times 4) \Rightarrow a . b = 6 + 4 + 12 \Rightarrow a . b = 22$
Hence, the required dot product is $22$

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If a→=2i^-2j^+3k^,b→=3i^-2j^+4k^ are two vectors then the dot product of vectorsa and b will be

If $\vec{a} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are two vectors then the dot product of vectors $a$ and $b$ will be