If the sides of a parallelogram are 2- -4- -5k- and - -2- -3k- then the unit vector parallel to one of the diagonals- is

The correct option is A #160; 1 7 ( 3î +6ĵ 2k̂ #160;) Let a =2î +4ĵ 5k̂ and b =î +2ĵ +3k̂ Then the diagonals of the parallelogram are ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Parallel

If the sides ...

Question

If the sides of a parallelogram are $2^i + 4^j - 5^k$ and $^i + 2^j + 3^k$ , then the unit vector parallel to one of the diagonals, 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}{7} (- 3^i + 6^j - 2^k)

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

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Solution

The correct option is A $\frac{1}{7} (3^i + 6^j - 2^k)$
Let $\to a = 2^i + 4^j - 5^k$ and $\to b =^i + 2^j + 3^k$
Then the diagonals of the parallelogram are
$\to p = \to a + \to b$ and $\to q = \to b - \to a$
$\Rightarrow \to p = 3^i + 6^j - 2^k$ and $\to q = -^i - 2^j + 8^k$
So, unit vectors along the diagonal are
$\frac{1}{7} (3^i + 6^j - 2^k)$ and $\frac{1}{\sqrt{69}} (-^i - 2^j + 8^k)$

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Similar questions

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

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

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)

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.

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If the sides of a parallelogram are 2^i+4^j−5^k and ^i+2^j+3^k, then the unit vector parallel to one of the diagonals, is

The correct option is A 17(3^i+6^j−2^k)Let →a=2^i+4^j−5^k and →b=^i+2^j+3^kThen the diagonals of the parallelogram are →p=→a+→b and →q=→b−→a⇒→p=3^i+6^j−2^k and →q=−^i−2^j+8^kSo, unit vectors along the diagonal are 17(3^i+6^j−2^k) and 1√69(−^i−2^j+8^k)

If the sides of a parallelogram are $2^i + 4^j - 5^k$ and $^i + 2^j + 3^k$ , then the unit vector parallel to one of the diagonals, is