© examsiri.com
Question : 19 of 101
Marks:
+1,
-0
Solution:
CONCEPT: - The scalar triple product of three vectors is zero if any two of them are equal
- If
is perpendicular to the vectors
then
â‹…=0 CALCULATION: Given:
=+, where
∣a]=∣≠0 Statement 1: is perpendicular to
(−) First let's find out
⋅(−)=(+)⋅(−) ⇒(+)⋅(−)=|a|2−⋅+⋅−||2 As we know that,
⋅=⋅ ⇒(+)⋅(−)=|a|2−∣2 ∵ It is given that
∣a⌉=∣b∣≠0 ⇒(+)⋅(−)=|a|2−||2=0 ⇒⋅(−)=0 Hence, statement 1 is true.
Statement 2: is perpendicular to
× First let's find out
⋅(×)=(+)⋅(×) ⇒(+)⋅(×)=⋅(×)+⋅(×) As we know that, the scalar triple product of three vectors is zero if any two of them are equal
⇒(+)⋅(×)=0 Hence, statement 2 is true.
Hence, the correct option is 3 .
© examsiri.com
Go to Question: