Question

Given A=3i+4j and B=6i+8j,which of the following statement is correct a)A*B=0 b)| A |\| B |=1\2 c)| A |=15 d)A·| B |=48

Answer 1

the correct option is B.
hope it helps u if any query plz let me know....

Answer 2

Answer:

Concept:

Systems of particles and rotational motion in physics

Explanation:

Given:

$\begin{aligned}&\overrightarrow{\mathrm{A}}=3 \overrightarrow{\mathrm{i}}+4 \overrightarrow{\mathrm{j}} \\&\overrightarrow{\mathrm{B}}=6 \overrightarrow{\mathrm{i}}+8 \overrightarrow{\mathrm{j}}\end{aligned}$

Solution:

a) A*B=0     Correct

        $\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}=(3 \overrightarrow{\mathrm{i}}+4 \overrightarrow{\mathrm{j}}) \times(6 \overrightarrow{\mathrm{i}}+8 \overrightarrow{\mathrm{j}}) \\\\ \overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}=24 \hat{\mathrm{k}}-24 \hat{\mathrm{k}}=0$

b) | A |\| B |=1\2  Correct

            $\frac{A}{B}=\frac{\sqrt{\left(3^{2}\right)+\left(4^{2}\right)}}{\sqrt{\left(6^{2}\right)+\left(8^{2}\right)}} \\\frac{\mathrm{A}}{\mathrm{B}}=\frac{5}{10}=\frac{1}{2}$

c) | A |=15   Wrong

$\mathrm{A}=\sqrt{\left(3^{2}\right)+\left(4^{2}\right)}=\sqrt{25}=5$

d) Wrong

$\vec{A} \cdot \vec{B}=(3 \vec{i}+4 \vec{j}) \cdot(6 \vec{i}+8 \vec{j}) \vec{A} \cdot \vec{B}=18+32=50$

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