Q.8 Three vectors are as follows: 𝑎𝑎⃗ = 3𝑖𝑖̂ − 10𝑗𝑗̂ + 7𝑘𝑘� 𝑏𝑏�⃗ = −9𝑖𝑖̂ + 6𝑗𝑗̂ − 47𝑘𝑘� 𝑐𝑐⃗ = 11𝑖𝑖̂ − 17𝑘𝑘� The value of �𝑎𝑎⃗ + 𝑏𝑏�⃗ � ⋅ 𝑐𝑐⃗ is (A) 614 (B) 746 (C) 2 (D) 134

To solve this problem, we first need to add vectors 𝑎𝑎⃗ and 𝑏𝑏⃗.

The sum of the vectors 𝑎𝑎⃗ and 𝑏𝑏⃗ is calculated as follows:

𝑎𝑎⃗ + 𝑏𝑏⃗ = (3𝑖 - 10𝑗 + 7𝑘) + (-9𝑖 + 6𝑗 - 47𝑘) = (3 - 9)𝑖 + (-10 + 6)𝑗 + (7 - 47)𝑘 = -6𝑖 - 4𝑗 - 40𝑘

Next, we need to find the dot product of the vector sum (𝑎𝑎⃗ + 𝑏𝑏⃗) and 𝑐𝑐⃗.

The dot product of two vectors is calculated as follows:

(𝑎𝑎⃗ + 𝑏𝑏⃗) ⋅ 𝑐𝑐⃗ = (-6𝑖 - 4𝑗 - 40𝑘) ⋅ (11𝑖 - 17𝑘) = -611 + -40 + -40*(-17) = -66 + 0 + 680 = 614

So, the value of (𝑎𝑎⃗ + 𝑏𝑏⃗) ⋅ 𝑐𝑐⃗ is 614. Therefore, the correct answer is (A) 614.