Question

the two vectors a and b that are parallel to each other are​

Answer 1

(A)  A = 3i+6j+9k , B = i+2j+3k are parallel vectors.

• A vector is a quantity that has both magnitude and direction.

• Parallel vectors: When the two vectors are in the same direction and have the same angle but vary in magnitude, they are known as the parallel vectors.

• In the given question:

                                       let 'x' be a scalar.

• In option(B), They are not parallel vectors as x(i + 2j + 3k) $\neq$ 3i-6j+9k.
• In option(C), They are not parallel vectors as x(i + 2j - 3k) $\neq$ 2i+3j+3k.
• In option(D), They are not parallel vectors as x(i - 2j - 3k) $\neq$ 2i+6j-9k.
• In option(A), They are vectors as x(i + 2j + 3k) = 3i+6j+9k.

                                                     Where, x = 3

Hence, option A is the correct answer.

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Answer 2

Answer:

Option A is the right  Answer

Explanation:

Tip-

• A physical quantity that has both directions and magnitude is referred to as a vector quantity.
• A unit vector is a vector whose magnitude is equal to one and is denoted by the lowercase letter "û" with a circumflex "hat" in it.
• Parallel vectors are those that are in the same direction, have the same angle, but have different magnitudes.

Given

ABCD option

Find

Right option

Step by Step Solution

First we will check with option A

For that lets take example

$\vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}$

$\vec{b}=b_{1} \hat{i}+b_{2} \hat{j}+b_{3} \hat{k}$

the above two vectors will be parallel only when their direction ratios are in proportion to each other

$Parallel \Longrightarrow \frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}=\frac{a_{3}}{b_{3}}$

Now coming to Option A,

$\vec{a}=3 \hat{i}+6 \hat{j}+9 \hat{k}$

$\vec{b}=1 \hat{i}+2 \hat{j}+3 \hat{k}$

$\Longrightarrow \frac{3}{1}=\frac{6}{2}=\frac{9}{3}=3$

Hence, the vectors are parallel.

Now check same thing with option B

$\vec{a}=3 \hat{i}-6 \hat{j}+9 \hat{k}$

$\vec{b}=1 \hat{i}+2 \hat{j}+3 \hat{k}$

$\Longrightarrow \frac{3}{1}\neq \frac{-6}{2}=\frac{9}{3}$

So its not parallel

Now Option C

$\vec{a}=2 \hat{i}+3 \hat{j}+3 \hat{k}$

$\vec{b}=1 \hat{i}+2 \hat{j}-3 \hat{k}$

$\Longrightarrow \frac{2}{1}\neq \frac{3}{2}\neq \frac{3}{-3}$

So its not parallel

Now Option D

$\vec{a}=2 \hat{i}+6 \hat{j}-9 \hat{k}$

$\vec{b}=1 \hat{i}-2 \hat{j}-3 \hat{k}$

$\Longrightarrow \frac{2}{1}\neq \frac{6}{-2}\neq \frac{-9}{-3}$

So its not parallel

Here only Option A satisfy all the condition

So Option A is the right  Answer

Final Answer

Option A is the right  Answer

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