A vector C when added to vectors A-3i-5j-k and B-2i-3j-4k gives a unit vector along the y-axis- Then- C is

The correct option is A 5i+3j+3k The given two vectors are A=3i 5j+k B=2i+3j 4k A unit vector along y axis is #160; ĵ According to the q ...

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Question

A vector $C$ when added to vectors $A = 3 ˆ i - 5 ˆ j + ˆ k$ and $B = 2 ˆ i + 3 ˆ j - 4 ˆ k$ gives a unit vector along the y-axis. Then, $C$ is

- 5 ˆ i + 3 ˆ j + 3 ˆ k

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5 ˆ i - 3 ˆ j - 3 ˆ k

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- 5 ˆ i + 2 ˆ j - 3 ˆ k

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5 ˆ i - 2 ˆ j - 3 ˆ k

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Solution

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3 i + 5 j + 2 k, 2 i - 3 j - 5 k a n d - 5 i - 2 j + 3 k

\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

\to P, \to Q

\to R

15

A B, B C

C A

A, B

C

\to O A = \to 2 i - \to j + \to 3 k

\to O B = \to 5 i + \to 3 j - \to 2 k

\to O C = - \to 2 i + \to 2 j + \to 3 k

_{1} = 2 ˆ i + 3 ˆ j + λ (5 ˆ i + 3 ˆ j - 3 ˆ k)

_{2} = ˆ i + 4 ˆ j + λ (3 ˆ i + 2 ˆ j + ˆ k) .

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