For any scalar ,
is a vector pointing in the same direction as
.
To force this vector to have the same length as another vector , first normalize
by dividing it by its norm,
then multiply this vector by the norm of , so that
To confirm that has the same length as
:
Given:
The expression is
To find:
The simplified form of the expression.
Solution:
We have,
The expression can be written as
Therefore, .
Answer:
Step-by-step explanation:
To add or subtract you need to make the denominator the same. To do this you need to find the least common multiple.
Answer:
3 cm
Step-by-step explanation:
When we enlarge or shrink an object, we perform a dilation. A dilation preserves the relationship between sides and the exact angle measure. This means the original and the enlargement are proportional and any missing lengths can be found through a proportion.
A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities. For example, we will compare height over length of the original rectangle to an equal ratio of height to length of the enlargement. Since we do not know height of the enlargement, we will use a variable to write:
I can now cross-multiply by multiplying numerator and denominator from each ratio.
I now solve for h by dividing by 9.
The new height is 3 cm.