Physics, asked by vidhi4087, 1 year ago

find component of a vector equal ICAP + 2 J cap + 3 k cap perpendicular to b vector equal ICAP + J cap + K cap​


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Answers

Answered by abhi178
22

here, \vec{a}=\hat{i}+2\hat{j}+3\hat{k}

\vec{b}=\hat{i}+\hat{j}+\hat{k}

we have to find component of vector a perpendicular to vector b

= \vec{a}-(\vec{a}.\hat{b})\hat{b}

here, \hat{b} denotes unit vector of b.

so, \hat{b}=\frac{\vec{b}}{|\vec{b}|}

= \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})

now, component of a perpendicular to vector b

= (\hat{i}+2\hat{j}+3\hat{k})-\left(\hat{i}+2\hat{j}+3\hat{k}.\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\right)\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})

=(\hat{i}+2\hat{j}+3\hat{k})-\left(\frac{1+2+3}{\sqrt{3}}\right)\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})

= (\hat{i}+2\hat{j}+3\hat{k})-2(\hat{i}+\hat{j}+\hat{k})

= -\hat{i}+\hat{j}

Answered by pinquancaro
9

Answer:

The component of vector a perpendicular to vector b is

C=\frac{(\sqrt{3}-6)i+(2\sqrt{3}-6)j+(3\sqrt{3}-6)k}{\sqrt{3}}

Explanation:

To find : The components of a \vec{a}=i+2j+3k perpendicular to C=-i+k

Solution :

The formula to find component of vector a perpendicular to vector b is given by,

C=\vec{a}-\frac{\vec{a}\cdot \vec{b}}{(|\vec{b}|)^2}\times \vec{b}

We know, \vec{a}=i+2j+3k and \vec{b}=i+j+k

|\vec{b}|=\sqrt{1^2+1^2+1^2}

|\vec{b}|=\sqrt{3}

|\vec{b}|^2=3

\vec{a}\cdot \vec{b}=1(1)+2(1)+3(1)

\vec{a}\cdot \vec{b}=6

Substitute the value in the formula,

C=i+2j+3k-\frac{6}{3}\times (i+j+k)

C=i+2j+3k-2\times (i+j+k)

C=i+2j+3k-2i-2j-2k

C=-i+0j+k

Therefore, The component of vector a perpendicular to vector b is C=-i+k

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