Question

Let →a=4^i+5^j−^k, →b=^i−4^j+5^k, and→c=3^i−^j−^k. Find a vector →d which is perpendicular to both →c and →b and →d. →a=21.

Answer 1

To find the vector →d perpendicular to both →c and →b, compute the cross product →c x →b. Adjust →d by a scalar if necessary to fulfill the dot product condition →d ⋅ →a = 21.

Step-by-step explanation:

The question asks to find a vector →d that is perpendicular to both vectors →c and →b, and also has a dot product of 21 with vector →a. To find a vector perpendicular to both →c and →b, we can use the cross product of →c and →b.

According to vector cross product rules, the cross product of two vectors results in a vector that is perpendicular to the plane containing the original vectors.

Using the cross product of →c and →b, we find →d. Once →d is determined, we can use the dot product of →d and →a to ensure it equals 21. If not, we adjust →d by a scalar multiple to meet the condition.

We can use the given unit vector cross product relationships (such as î x î = 0 and î x ı = â) to compute the cross product and then ensure that the dot product with →a equals 21.