First slide

Vectors

Question

Consider the following statements A and B given below and identify the correct answer.
A) Vectors $\hat{i} + 3 \hat{j} + 5 \hat{k}$ and $2 \hat{i} + 6 \hat{j} + 10 \hat{k}$ are parallel
B) $\hat{i} + \hat{j} + \hat{k}$ represents a unit vector

Moderate

A

Both A and B false
B

A is true B is false
C

B is true but A is false
D

Both A and B are false

Solution

If the vectors $\large (a_1\hat i +a_2\hat j+ a_3\hat k)$ and $\large (b_1\hat i +b_2\hat j+ b_3\hat k)$ are parallel then $\large \frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac {a_3}{b_3}$ . In statement (A) , $\large \frac{1}{2}=\frac{3}{6}=\frac {5}{10}$ So Statement (A)is true
Magnitude of unit vector is 1 .
But in statement (B) , magnitude of the vector $\large (\vec i+\vec j+\vec k)$ is $\large (\sqrt{{1^2}+{1^2}+{1^2}})$ = √3 .So statement-(B) is false
Therefore option - (2) is right.

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