Projection of Vector A on Vector B
Given vectors:
\[ \vec{A} = \hat{i} - 2\hat{j} + \hat{k}, \quad \vec{B} = 4\hat{i} - 4\hat{j} + 7\hat{k} \]
Formula Used
Scalar Projection of A on B:
\[ \text{Projection} = \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|} \]
Step 1: Dot Product
\[ \vec{A} \cdot \vec{B} = (1)(4) + (-2)(-4) + (1)(7) \]
\[ = 4 + 8 + 7 = 19 \]
Step 2: Magnitude of B
\[ |\vec{B}| = \sqrt{4^2 + (-4)^2 + 7^2} \]
\[ = \sqrt{16 + 16 + 49} = \sqrt{81} = 9 \]
Final Answer
\[ \text{Projection of } \vec{A} \text{ on } \vec{B} = \frac{19}{9} \]
Answer: 19/9
Important Questions from Mixed Topic (CUET PG)
- Who was the founder of Bolshevik Communist party?
- What is the key guide to statecraft in the realist tradition?
- Chronologically arrange the events in the Cold War period.
A. Berlin Wall is constructed
B. Communist China joins the UN
C. Soviet invasion of Czechoslovakia
D. Berlin Blockade
Choose the correct answer from the options given below: Morgenthau's principles of political realism are:
A. Politics is rooted in permanent and unchanging human nature which is basically self centred, self-regarding and self-interested
B. Politics is an autonomous sphere of action and cannot therefore be reduced to morals
C. International Politics is an arena of conflicting self-interests
D. The ethics of international relations is situational ethics which is very different from private morality
Choose the correct answer from the options given below:Who among the following political thinkers consider the anarchical self help system to be a compelling factor for States to maximise their relative power positions?
