We have,
∣∣→a∣∣=√26
∣∣∣→b∣∣∣=7
∣∣∣→a×→b∣∣∣=35
Since,
∣∣∣→a×→b∣∣∣=∣∣→a∣∣∣∣∣→b∣∣∣sinθ
Thus,
35=√26×7×sinθ
sinθ=5√26
We know that
→a⋅→b=∣∣→a∣∣∣∣∣→b∣∣∣cosθ
Therefore,
→a⋅→b=√26×7×√1−sin2θ
→a⋅→b=√26×7×√1−2526
→a⋅→b=√26×7×√126
→a⋅→b=7
Hence, this is the answer.