Question

Vectors A and B are given as A = 10i - 2tj and vector B = 5i + 5j . Find the time when A is perpendicular to B


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Answer 1

Answer:

5 seconds

Step-by-step explanation:

Given :

$\vec A = 10i - 2tj$

$\vec B = 5i + 5j$

To find :

the time when A is perpendicular to B

Solution :

We know that

$\boxed{\begin{array}{cc} \text{If } \vec A \perp \vec B \text{ then,}\\{\vec A.\vec B = 0}\end{array}}$

Dot product is,

$\boxed{\begin{array}{cc} \text{ \vec A = a_xi + a_yj+a_zk and \vec B = b_xi+b_yj+b_zk }\\\text{then}\\\vec A.\vec B = a_x.b_x+a_y.b_y+a_z.b_z\end{array}}$

So, dot product of A and B is,

$\implies \vec A.\vec B = (10i-2tj).(5i+5j)$

$\implies \vec A.\vec B = 50-10t = 0$

$\implies 50 - 10t = 0$

$\implies 50 = 10t$

$\implies t = \dfrac{50}{10}$

$\therefore \underline{\boxed{\bold {t = 5}}}$

Hope it helps!!

Answer 2

From the given question the correct answer is:

the time is 5 sec when A is perpendicular to B

$[tex]\vec A = 10i - 2tj$[/tex]

$[tex]\vec B = 5i + 5j$[/tex]

To find :

the time when A is perpendicular to B

Solution :

Now,

$[tex]\boxed{\begin{array}{cc} \text{If } \vec A \perp \vec B \text{ then,}\\{\vec A.\vec B = 0}\end{array}}$[/tex]

Dot product is

$[tex]\boxed{\begin{array}{cc} \text{ \vec A = a_xi + a_yj+a_zk and \vec B = b_xi+b_yj+b_zk }\\\text{then}\\\vec A.\vec B = a_x.b_x+a_y.b_y+a_z.b_z\end{array}}$[/tex]

dot product of A and B is,

$[tex]\implies \vec A.\vec B = (10i-2tj).(5i+5j)$$\implies \vec A.\vec B = 50-10t = 0$$\implies 50 - 10t = 0$$\implies 50 = 10t$$\implies t = \dfrac{50}{10}$$\therefore \underline{\boxed{\bold {t = 5}}}$[/tex]