Unit vector parallel to resultant of vectors vec A = 4hat{i} + 3hat{j} + 6hat{k} and vec B =

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3-1.Vectors

medium

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

A$\frac{1}{7}(3\hat i + 6\hat j - 2\hat k)$

B$\frac{1}{7}(3\hat i + 6\hat j + 2\hat k)$

C$\frac{1}{{49}}(3\hat i + 6\hat j - 2\hat k)$

D$\frac{1}{{49}}(3\hat i - 6\hat j + 2\hat k)$

Solution

(a) Resultant of vectors $\overrightarrow A $ and $\overrightarrow B $
$\overrightarrow R = \overrightarrow A + \overrightarrow B = 4\hat i + 3\hat j + 6\hat k – \hat i + 3\hat j – 8\hat k$
$\overrightarrow R = 3\hat i + 6\hat j – 2\hat k$
$\hat R = \frac{{\overrightarrow R }}{{|\vec R|}} = \frac{{3\hat i + 6\hat j – 2\hat k}}{{\sqrt {{3^2} + {6^2} + {{( – 2)}^2}} }} = \frac{{3\hat i + 6\hat j – 2\hat k}}{7}$

Standard 11

Physics

Explain the parallelogram method for vector addition. Also explain that this is comparable to triangle method.

medium

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easy

Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

medium

(AIEEE-2002)

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hard

(JEE MAIN-2024)

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hard

(AIIMS-2016)

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

Solution

Similar Questions

Explain the parallelogram method for vector addition. Also explain that this is comparable to triangle method.

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$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is