The vector a-1-72-3-6k- - b-1-73-6-2k- - c-1-76-2-3k- form

The correct option is A an orthonormal system a⃗.b⃗=0 b⃗.c⃗=0 c⃗.a⃗=0 So a⃗,b⃗ amp; #160; c⃗ #160; ⊥ are to each other.Therefo ...

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Standard XII

Mathematics

Arithmetic Progression

The vector ...

Question

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

a right handed system

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a left handed system

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an orthogonal system

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an orthonormal system

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Solution

The correct option is A an orthonormal system
$\to a . \to b = 0$
$\to b . \to c = 0$
$\to c . \to a = 0$
So $\to a, \to b$ & $\to c ⊥$ are to each other.
Therefore they form orthonormal system.

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Similar questions

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. 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.

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. Which of the following is correct for the vectors

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

and

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

Q. Which of the following is correct for the vectors

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

and

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

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The vector →a=1/7(2^i+3^j+6^k) ,→b=1/7(3^i−6^j+2^k) , →c=1/7(6^i+2^j−3^k) form

The correct option is A an orthonormal system→a.→b=0→b.→c=0→c.→a=0So →a,→b & →c⊥ are to each other.Therefore they form orthonormal system.

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

The correct option is A an orthonormal system
$\to a . \to b = 0$
$\to b . \to c = 0$
$\to c . \to a = 0$
So $\to a, \to b$ & $\to c ⊥$ are to each other.
Therefore they form orthonormal system.