Q.1 (iv) The perpendicular distance of the plane r · (3i + 4j + 12k) = 78 , from the origin is _____. A. 4 B. 5 C. 6 D. 8

Answer: C. 6 Answer: (c) 6 For the plane r · n = d , the distance from the origin is |d|/|n| . Here |n| = √(9 + 16 + 144) = √(169) = 13 , so the distance is 78/13 = 6 units.

The perpendicular distance of the plane \(\bar{r} \cdot (3\hat{i} + 4\hat{j} + 12\hat{k}) = 78\), from the origin is _____.

Q.1 (iv) The perpendicular distance of the plane \(\bar{r} \cdot (3\hat{i} + 4\hat{j} + 12\hat{k}) = 78\), from the origin is _____.

A. 4

B. 5

C. 6

D. 8

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: C. 6

Answer: (c) 6

For the plane \(\bar{r} \cdot \bar{n} = d\), the distance from the origin is \(\frac{|d|}{|\bar{n}|}\). Here \(|\bar{n}| = \sqrt{9 + 16 + 144} = \sqrt{169} = 13\), so the distance is \(\frac{78}{13} = 6\) units.

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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The perpendicular distance of the plane \(\bar{r} \cdot (3\hat{i} + 4\hat{j} + 12\hat{k}) = 78\), from the origin is _____.

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