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Vector Equation for Straight Line

which of the ...

Question

which of the following vector is perpendicular to the vector a= 2i+3j+4k ? a) i+j+k b) 4i+3j-2k c) i-3j+k d) i+2j-2k

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Q. Prove that the following vectors are coplanar:
(i)

2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}

\hat{i} + \hat{j} + \hat{k}, 2 \hat{i} + 3 \hat{j} - \hat{k} and - \hat{i} - 2 \hat{j} + 2 \hat{k}

Q. Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
(i)

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} + 2 \hat{k}

\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} - 2 \hat{k}

\vec{a} = 11 \hat{i}, \vec{b} = 2 \hat{j}, \vec{c} = 13 \hat{k}

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

Q. Show the each of the following triads of vectors are coplanar:
(i)

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

2 ¯ i - 3 ¯ j + 4 ¯ ¯ ¯ k, ¯ i - 2 ¯ j + 3 ¯ ¯ ¯ k

3 ¯ i + ¯ j - 2 ¯ ¯ ¯ k

Q. For what value of λ are the vectors

\vec{a} and \vec{b}

perpendicular to each other if
(i)

\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 4 \hat{i} - 9 \hat{j} + 2 \hat{k}

\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 5 \hat{i} - 9 \hat{j} + 2 \hat{k}

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} and \vec{b} = 3 \hat{i} + 2 \hat{j} - λ \hat{k}

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

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