Question:

which is the true of the following ?
(A)Any vector \(\overrightarrow{r}\) in space can be written as \((\overrightarrow{r}.\hat{i})\hat{i}+(\overrightarrow{r}.\hat{j})\hat{j}+(\overrightarrow{r}.\hat{k})\hat{k}\) 
(B)If  \(\overrightarrow{a}\)  is perpendicular to  \(\overrightarrow{b}\)\(|\overrightarrow{a}+\overrightarrow{b}|^2=|\overrightarrow{a}|^2+|\overrightarrow{b}|^2\) 
 
(C)If \(|\overrightarrow{a}|=2,|\overrightarrow{b}|=1 \) and \(\overrightarrow{a}.\overrightarrow{b}=1 \) ,the value of \((3\overrightarrow{a}-5\overrightarrow{b}).(2\overrightarrow{a}+7\overrightarrow{b})\) ia 1
(D) \(\overrightarrow{a}=5\hat{i}-\hat{j}-3\hat{k}\) and \(\overrightarrow{b}=\hat{i}+3\hat{j}-5\hat{k}\), is the angle between \(\overrightarrow{a}+\overrightarrow{b}\) and \(\overrightarrow{a}-\overrightarrow{b}\) is \(60\degree\)
Choose the correct answer from the options given below:
 

Updated On: May 21, 2024
  • (A) and (B) Only
  • (B) Only
  • (C) Only
  • (D) Only
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The Correct Option is A

Solution and Explanation

The correct option is (A):(A) and (B) Only
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