For any vector vec a , the value of (vec atimeshat i )^2+ (vec atimeshat j )^2+ (vec atimeshat k )^2 is equal to :

Vector Algebra: For any vector vec a , the value of (vec atimeshat i )^2+ (vec… | AIEEE 2005

AIEEE 2005 (Offline)Question 1

For any vector $\vec a$, the value of $\left(\vec a\times\hat i\right)^{2}+\left(\vec a\times\hat j\right)^{2}+\left(\vec a\times\hat k\right)^{2}$ is equal to :

Vector Algebra

$3a^{2}$$a^{2}$$2a^{2}$✓ Correct answer$4a^{2}$

Solution

$|\vec a\times\hat i|^2=a^2-a_1^2$, etc.; summing gives $3a^2-a^2=2a^2$.

Vector Algebra - JEE Mathematics question (AIEEE 2005 (Offline))

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