VECTOR ALGEBRA

Classify the following as scalar and vector quantities:

(i) time period (ii) distance (iii) force (iv) velocity (v) work done

• (i) scalar

• (ii) vector

• (iii) vector

• (iv) scalar

• (v) scalar

Tags

CCSS.HSN.VM.A.1

Which of the following is correct

• $\overrightarrow{a},\ \overrightarrow{c},\ and\ \ \overrightarrow{d},$ are collinear

• $\overrightarrow{a}\ and\ \ \overrightarrow{c}\ \$ are equal

• $\overrightarrow{a}\ =-\overrightarrow{d}$

• $\overrightarrow{b},\ \overrightarrow{c}\ ,\ and\ \ \overrightarrow{d}$ are coinitial

• $\overrightarrow{c}=-\overrightarrow{d}$

Tags

CCSS.HSN.VM.A.1

A unit vector of

 $\overrightarrow{a}=i\ +\ j\ +\ 2k$  is 

•  $\frac{1}{2}i\ +\ \frac{1}{2}j\ +\ 2k$  

•  $\frac{1}{\sqrt{2}}i\ +\frac{1}{\sqrt{2}}j\ +\ \sqrt{2}k$  

•  $\frac{\sqrt{2}}{4}i\ +\ \frac{\sqrt{2}}{4}j\ +\ \frac{\sqrt{2}}{2}k$  

•  $\frac{1}{4}i\ +\ \frac{1}{4}j\ +\frac{\sqrt{2}}{4}k\ \$  

What is the angle between vectors u and v, where

 $\overrightarrow{u}=\ 2i\ -\ 3j\ +\ 4k\ \ and\ \overrightarrow{\ v}=\ -4i\ +\ 6j\ -\ 8k$  

(a)  

Find the projection of vector

 $\overrightarrow{p}\ =\ i\ +\ 3j\ +\ 7k\ \ on\ the\ vector\ \ \overrightarrow{q}\ =\ 7i\ -\ j\ +\ 8k$  

(a)  

If

 $\overrightarrow{a}=2i\ +\ 2j\ +\ 3k,\ \ \overrightarrow{b}=-i\ +\ 2j\ +\ k,\ and\ \ \overrightarrow{c}=3i\ +\ j\ \$ such that  $\overrightarrow{a}\ +\ m\overrightarrow{b}$  is perpendicular to  $\overrightarrow{c}$ ,  then find the value of m

(a)  

  $Given\ \overrightarrow{p}=i-7j+7k\ \ and\ \ \overrightarrow{q}=3i-2j+2k$  

Find  $\overrightarrow{p}\ \times\ \overrightarrow{q}$  

• 19i + 19j

• 19i + 19k

• 19i + 19k

• 19j + 19k

 $\overrightarrow{ }$  Let the vectors   $\overrightarrow{a}\ \ and\ \ \ \overrightarrow{b}$       such that  $\left|\overrightarrow{a}\right|=3\ \ and\ \ \ \left|\overrightarrow{b}\right|=\frac{\sqrt{2}}{3}$ . What is the angle between  $\overrightarrow{a}\ \ and\ \ \ \overrightarrow{b}$  if   $\overrightarrow{a\ }\ \times\ \overrightarrow{b\ }$  is a unit vector ?

• pi/6

• pi/4

• pi/3

• pi/2