First slide

Scalars and Vectors

Question

Given $A = 3 \hat{i} + 4 \hat{j}$ and $B = 6 \hat{i} + 8 \hat{j}$ , which of the following statement is correct?

Moderate

A

$A \times B = 0$
B

$\frac{| A |}{| B |} = \frac{1}{3}$
C

|A| = 15
D

$A \cdot B = 48$

Solution

$| A | = \sqrt{9 + 16} = 5$
and $| B | = \sqrt{36 + 64} = 10 .$
$B = 2 A$ or B is parallel to A. Ratio of their coefficients are equal, so they are parallel or their cross product is zero.

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