Vectors a hat{i}+b hat{j}+hat{k} and 2 hat{i} | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

For two perpendicular vectors

$(a \hat{i}+b \hat{j}+\hat{k}) \cdot(2 \hat{i}-3 \hat{j}+4 \hat{k})=0$

$2 a-3 b+4=0$

On solving, $2 a-3 b=-4$

Vedclass · Accepted Answer

$1$

Vedclass · Answer

For two perpendicular vectors

$(a \hat{i}+b \hat{j}+\hat{k}) \cdot(2 \hat{i}-3 \hat{j}+4 \hat{k})=0$

$2 a-3 b+4=0$

On solving, $2 a-3 b=-4$

Also given

$3 a+2 b=7$

We get $a =1, b =2$

$\frac{ a }{ b }=\frac{ x }{2} \Rightarrow x =\frac{2 a }{ b }=\frac{2 	imes 1}{2}$

$\Rightarrow x =1$

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 $3 a+2 b=7$, the ratio of a to $b$ is $\frac{x}{2}$. The value of $x$ is $..............$

Similar Questions

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ a unit vector perpendicular to both $\overrightarrow A $ and $\overrightarrow B $ will be

Find the angle between two vectors with the help of scalar product.

For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})$, $\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})$, if $\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0$, them value of $\mathrm{x}$ is. . . . . ..

If $a + b + c =0$ then $a \times b$ is

$\overrightarrow A $ and $\overrightarrow B $ are two vectors given by $\overrightarrow A = 2\widehat i + 3\widehat j$ and $\overrightarrow B = \widehat i + \widehat j$. The magnitude of the component (projection) of $\overrightarrow A$ on $\overrightarrow B$ is