Question 88: Motion in 2D & Vectors

Question

Two vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other. When $3 \mathrm{a}+2 \mathrm{~b}=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is

Accepted Answer

$$ \vec{A}=a \hat{i}+b \hat{j}+\hat{k} ; \vec{B}=2 \hat{i}-3 \hat{j}+4 \hat{k} $$
As the two vectors are perpendicular to eaÃÂ§h other
$$ \begin{array}{ll} 	herefore & \vec{A} \cdot \vec{B}=0 \ 	herefore & 2 a-3 b+4=0 \ & 3 a+2 b=7 
\,\,\,\,\,\,\,\,	ext { ....(given) }
\end{array} $$
Solving for a and b , we get
$$ \begin{aligned} & a=1, b=2 \ 	herefore \quad & a: b=1: 2 \end{aligned} $$
$	herefore \quad$ value of x is 1

Answer

zero

Answer

2

Answer

1

Answer

4

Motion in 2D & Vectors

Two vectors a \hat{i}+b \hat{j}+\hat{k} and 2 \hat{i}-3 \hat{j}+4 \hat{k} are perpendicular to each other. When 3 \mathrm{a}+2 \mathrm{~b}=7, the ratio of a to b is \frac{x}{2}. The value of x is

Choose the correct answer: