The unit vector parallel to the resultant of the vectors A -4 -3 -6 k- andB -3 -8 k- isA- 1-73 -6 -2 k-B- 1-73 -6 -2 k-C- 1-493 -6 -2 k-D- 1-493 -6 -2 k-

The correct option is A 1/7(3î+6ĵ 2k̂) Resultant of vectors A⃗ and B⃗ R⃗=A⃗+B⃗=4î+3ĵ+6k̂ î+3ĵ 8k̂ R⃗=3î+6ĵ 2k̂ R̂=R⃗/|R⃗|=3î+6ĵ 2k̂/√(3^2+6^2 +( 2)^2)=3î+6ĵ 2k ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

The unit vect...

Question

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

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

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

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

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

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Solution

The correct option is A
$\frac{1}{7} (3^i + 6^j - 2^k)$

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

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Similar questions

Q. The vector

\to a = 1 / 7 (2^i + 3^j + 6^k)

\to b = 1 / 7 (3^i - 6^j + 2^k)

\to c = 1 / 7 (6^i + 2^j - 3^k)

form

Let $\to a = \frac{1}{7} (2^i + 3^j + 6^k), \to b = \frac{1}{7} (6^i + 2^j - 3^k), \to c = c_{1}^i + c_{2}^j + c - 3^k$ and matrix $A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{7} & \frac{3}{7} & \frac{6}{7} \frac{6}{7} & \frac{2}{7} & - \frac{3}{7} c_{1} & c_{2} & c_{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$
If $A A^{T} = I, t h e n \to c$ is equal to

Q. Show that each of the given three vectors is a unit vector:

\frac{1}{7} (2^i + 3^j + 6^k), \frac{1}{7} (3^i - 6^j + 2^k), \frac{1}{7} (6^i + 2^j - 3^k)

.
Also, show that they are mutually perpendicular to each other.

Q. Show that each of the three given vectors is a unit vectors. also Show that they are mutually

⊥

to each other.

\to a = \frac{1}{7} (2^i + 3^j + 6^k)

\to b = \frac{1}{7} (3^i - 6^j + 2^k)

\to c = \frac{1}{7} (6^i + 2^j - 3^k)

Q. A unit vector perpendicular to the plane of

a = 2^i - 6^j - 3^k, b = 4^i + 3^j -^k

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The unit vector parallel to the resultant of the vectors →A=4^i+3^j+6^k and →B=−^i+3^j−8^k is

The correct option is A 17(3^i+6^j−2^k) Resultant of vectors →A and →B →R=→A+→B=4^i+3^j+6^k−^i+3^j−8^k →R=3^i+6^j−2^k ^R=→R|→R|=3^i+6^j−2^k√32+62+(−2)2=3^i+6^j−2^k7

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

The correct option is A
$\frac{1}{7} (3^i + 6^j - 2^k)$

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