Statement I The projection of the vector a =2 hat i +3 hat j +2 hat k on the vector b = hat i +2 hat j + hat k is (5/3) √6 Statement II The projection of vector a on vector b is (1/| a |)( a ⋅ b )

Question

Statement I The projection of the vector a =2 hat i +3 hat j +2 hat k on the vector b = hat i +2 hat j + hat k is (5/3) √6 Statement II The projection of vector a on vector b is (1/| a |)( a ⋅ b ) (A) Statement I is true; statement II is true; statement II is a correct explanation for statement I (B) Statement I is true; statement II is true; statement II is not a correct explanation for statement I (C) Statement I is true; statement II is false (D) Statement I is false; statement II is true

Tardigrade Admin · Accepted Answer

The projection of vector a on the vector b is given by ((a ⋅ b)/|b|)=((2 × 1+3 × 2+2 × 1)/√(1)2+(2)2+(1)2)=(10/√6)=(5/3) √6

Q. Statement I The projection of the vector $a = 2 \hat{i} + 3 \hat{j} + 2 \hat{k}$ on the vector $b = \hat{i} + 2 \hat{j} + \hat{k}$ is $\frac{5}{3} 6$
Statement II The projection of vector a on vector $b$ is $\frac{1}{∣ a ∣} (a \cdot b)$

Statement I is true; statement II is true; statement II is a correct explanation for statement I

Statement I is true; statement II is true; statement II is not a correct explanation for statement I

Statement I is true; statement II is false

Statement I is false; statement II is true

The projection of vector $a$ on the vector $b$ is given by
$\frac{( a \cdot b )}{∣ b ∣} = \frac{( 2 \times 1 + 3 \times 2 + 2 \times 1 )}{( 1 ) ^{2} + ( 2 ) ^{2} + ( 1 ) ^{2}} = \frac{10}{6} = \frac{5}{3} 6$

Q. Statement I The projection of the vector a=2i^+3j^​+2k^ on the vector b=i^+2j^​+k^ is 35​6​ Statement II The projection of vector a on vector b is ∣a∣1​(a⋅b)