The vectors a = xi + yj + zk and b = j are such that a, c, b form a right-handed system. Then c is: - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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The vectors a = x \hat{i} + y \hat{j} + z \hat{k} and b = \hat{j} are such that a, c, b form a right-handed system. Then c is:

Solution & Step-by-step Explanation

In a right-handed system (a, c, b), the vector c must be given by b \times a (following the cyclic order). c = b \times a = \hat{j} \times (x \hat{i} + y \hat{j} + z \hat{k}) Using cross product properties: \hat{j} \times \hat{i} = - \hat{k} \hat{j} \times \hat{j} = 0 \hat{j} \times \hat{k} = \hat{i} So: c = x (- \hat{k}) + y (0) + z (\hat{i}) = z \hat{i} - x \hat{k}

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The vectors a = x \hat{i} + y \hat{j} + z \hat{k} and b = \hat{j} are such that a, c, b form a right-handed system. Then c is:

z \hat{i} - x \hat{k}

0

y \hat{j}

- z \hat{i} + x \hat{k}

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