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Multiplication with Vectors

Given a=i+j...

Question

Given $a = i + j - k, b = - i + 2 j + k$ and $c = - i + 2 j - k$ a unit vector perpendicular to both $a + b$ and $b + c$ is

i

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j

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k

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(i + j + k) / \sqrt{3}

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Solution

The correct option is C $k$
$a + b = 3 j, b + c = - 2 i + 4 j$
Vector perpendicular to both is given by, $∣ ∣ ∣ ∣ \begin{matrix} i & j & k 0 & 3 & 0 - 2 & 4 & 0 \end{matrix} ∣ ∣ ∣ ∣ = 6 k$
Hence required unit vector is, $k$

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a = i + j - k, b = - i + 2 j + k

c = - i + 2 j - k .

a + b

b + c

\vec{a} = \hat{i} + \hat{j} - \hat{k}, \vec{b} = - \hat{i} + 2 \hat{j} + 2 \hat{k} and \vec{c} = - \hat{i} + 2 \hat{j} - \hat{k},

\vec{a} + \vec{b} and \vec{b} - \vec{c}

\hat{i}

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\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} - \hat{j} + 3 \hat{k} and \vec{c} = \hat{i} - 2 \hat{j} + \hat{k},

2 \vec{a} - \vec{b} + 3 \vec{c .}

i + 2 j + k

i + 2 j + k

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[\vec{a} \vec{b} \vec{c}]

\vec{a} = 2 \hat{i} - 3 \hat{j}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and \vec{c} = 3 \hat{i} - \hat{k}

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} and \vec{c} = \hat{j} + \hat{k}

\vec{a} = 2 \hat{i} + 3 \hat{j} + \hat{k}, \vec{b} = \hat{i} - 2 \hat{j} + \hat{k} and \vec{c} = - 3 \hat{i} + \hat{j} + 2 \hat{k}

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