Find the area of triangle whose vertices are $straight P left right arrow left parenthesis 1 comma space 1 comma space 1 right parenthesis comma space straight Q left right arrow left parenthesis 2 comma space 2 comma space 2 right parenthesis space and space straight R left right arrow left parenthesis 2 comma space minus 1 comma space 2 right parenthesis.$

Solution

Here, P, Q and R are the vertices of a triangle.
Therefore $PQ with rightwards arrow on top space and space PR with rightwards arrow on top$ represent the sides of triangle as shown in the figure.

We have,
$PQ with rightwards arrow on top space equals space left parenthesis 2 minus 1 right parenthesis straight i with hat on top plus left parenthesis 2 minus 1 right parenthesis straight j with hat on top plus left parenthesis 2 minus 1 right parenthesis straight k with hat on top space equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top$
$PR with rightwards arrow on top space equals left parenthesis 2 minus 1 right parenthesis straight i with hat on top plus left parenthesis negative 1 minus 1 right parenthesis straight j with hat on top plus left parenthesis 2 minus 1 right parenthesis straight k with hat on top equals straight i with hat on top minus 2 straight j with hat on top plus straight k with hat on top$
Now, area of triangle PQR = $1 half open vertical bar stack P Q with rightwards harpoon with barb upwards on top cross times stack P R with rightwards harpoon with barb upwards on top close vertical bar space$
$PQ with rightwards harpoon with barb upwards on top space cross times stack P R with rightwards harpoon with barb upwards on top space equals space open vertical bar table row i j k row 1 1 1 row 1 cell negative 2 end cell 1 end table close vertical bar space equals space 3 i with hat on top space minus space 3 k with hat on top space space space space a n d open vertical bar stack P Q with rightwards harpoon with barb upwards on top space cross times stack P R with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of left parenthesis 3 right parenthesis squared minus open parentheses 3 close parentheses squared end root space equals space 3 square root of 2 space$
Therefore, area of $increment PQR comma space$ = $1 half cross times 3 square root of 2 space equals space fraction numerator 3 over denominator square root of 2 end fraction u n i t s$

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

What is a scalar quantity?

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

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