Answer
Verified
480.3k+ views
Hint: The cross product two unit vector is the vector perpendicular to both of them. And, the dot product of two unit vectors in the same direction is equal to 1.
We have , an equation \[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]. The vectors i, j and k are the vectors in x-direction , y-direction and the z-direction.
There are three operations involved in these expressions.
1) Cross product of two unit vector
2) Dot product of two unit vector
3) Addition
Cross product of any two unit vector can be given by remembering small sequence
$
{\text{i}} \to {\text{j}} \to {\text{k}} \to {\text{i}} \\
{\text{i}} \times {\text{j = k}} \\
{\text{j}} \times {\text{k = i}} \\
{\text{k}} \times {\text{i = j}} \\
$
Applying it on the given equation, we have
\[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]= k.k + i.i
Now, the dot product of two vectors is equal to the multiplication of length of the two vectors and cosine of the angle between them.
${\text{a}}{\text{.b = |a||b|cos}}\theta $ where $\theta $ is the angle between vectors a and b.
The length of the unit vector is 1. And if angle is 0 degree, then a.b = 1.
So,
\[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]= k.k + i.i
=1 + 1
= 2
The value of \[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]is 2.
Note: In these types of questions, we need to start with solving the brackets , then the whole expression. The cross product of two unit vectors in the same direction is zero. The dot product of two perpendicular unit vectors is zero.
We have , an equation \[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]. The vectors i, j and k are the vectors in x-direction , y-direction and the z-direction.
There are three operations involved in these expressions.
1) Cross product of two unit vector
2) Dot product of two unit vector
3) Addition
Cross product of any two unit vector can be given by remembering small sequence
$
{\text{i}} \to {\text{j}} \to {\text{k}} \to {\text{i}} \\
{\text{i}} \times {\text{j = k}} \\
{\text{j}} \times {\text{k = i}} \\
{\text{k}} \times {\text{i = j}} \\
$
Applying it on the given equation, we have
\[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]= k.k + i.i
Now, the dot product of two vectors is equal to the multiplication of length of the two vectors and cosine of the angle between them.
${\text{a}}{\text{.b = |a||b|cos}}\theta $ where $\theta $ is the angle between vectors a and b.
The length of the unit vector is 1. And if angle is 0 degree, then a.b = 1.
So,
\[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]= k.k + i.i
=1 + 1
= 2
The value of \[\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}\]is 2.
Note: In these types of questions, we need to start with solving the brackets , then the whole expression. The cross product of two unit vectors in the same direction is zero. The dot product of two perpendicular unit vectors is zero.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE