Show the vectors A- -2- -3-k- and B- -6- -9- -3 k- are parallel-

We know that if two vectors are parallel their cross product is zero.Here, #160; A⃗×B⃗ = (2î 3ĵ k̂)×( 6 î+9ĵ+3k̂) = 3 (2î 3ĵ k̂)×( 2 î+3ĵ+k̂) = 0 Th ...

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Standard XII

Physics

Multiplication with Vectors

Show the vect...

Question

Show the vectors $\to A = 2^i - 3^j -^k$ and $\to B = - 6^i + 9^j + 3^k$ are parallel.

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Solution

We know that if two vectors are parallel their cross product is zero.

Here,
$\to A \times \to B = (2^i - 3^j -^k) \times (- 6^i + 9^j + 3^k) =$ $- 3 (2^i - 3^j -^k) \times (- 2^i + 3^j +^k) = 0$
Therefore, they are parallel.

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Q. Prove that the vectors

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- 6^i + 9^j + 3^k

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and

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Q. Calculate the angle between the vectors

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If $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b,$ then a possible value of $(\to a + \to b) . (- 7^i + 2^j + 3^k)$ is

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\to a =^i - 3^k, . \to b = 2^j -^k, \to c = 2^i - 3^j + 2^k

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Show the vectors →A=2^i−3^j−^k and →B=−6^i+9^j+3 ^k are parallel.

We know that if two vectors are parallel their cross product is zero.Here, →A×→B=(2^i−3^j−^k)×(−6^i+9^j+3^k)=−3(2^i−3^j−^k)×(−2^i+3^j+^k)=0Therefore, they are parallel.

Show the vectors $\to A = 2^i - 3^j -^k$ and $\to B = - 6^i + 9^j + 3^k$ are parallel.

We know that if two vectors are parallel their cross product is zero.

Here,
$\to A \times \to B = (2^i - 3^j -^k) \times (- 6^i + 9^j + 3^k) =$ $- 3 (2^i - 3^j -^k) \times (- 2^i + 3^j +^k) = 0$
Therefore, they are parallel.