- Two vectors, a and b, are perpendicular to each other.
- The magnitude of vector a is 2 and the magnitude of vector b is 3.
- The vector cx a is equal to vector b.


To find the least value of 10|c - a|, we need to understand the properties of vectors and their dot product.


- Two vectors are perpendicular to each other if their dot product is zero.
- The dot product of two vectors a and b is given by a·b = |a| |b| cosθ, where θ is the angle between the vectors.
- The magnitude of a vector can be found using the formula |a| = √(a1^2 + a2^2 + a3^2).


- The magnitude of vector a is 2: |a| = 2.
- The magnitude of vector b is 3: |b| = 3.
- The vector cx a is equal to vector b: cx a = b.


Since cx a = b, we can find the value of c by dividing both sides of the equation by a:
c = b/a.


We can substitute the given magnitudes of vectors a and b into the equation to find the value of c:
c = b/a = 3/2 = 1.5.


To find the value of |c - a|, we need to subtract vector a from vector c and then find its magnitude:
c - a = 1.5 - 2 = -0.5.

The magnitude of vector c - a is given by:
|c - a| = √((-0.5)^2) = √(0.25) = 0.5.


To find the least value of 10|c - a|, we multiply the magnitude by 10:
10|c - a| = 10 * 0.5 = 5.

Therefore, the least value of 10|c - a| is 5.