Question

find the angle between a vector to icap + 3 j cap + k cap and b vector 4 icap + 4 j cap + k cap is 90 degree then the value of a is

Answer 1

To find the angle between two vectors, we can use the dot product formula. Given vectors a = ai + aj + ak and b = 4i + 4j + k with an angle of 90 degrees between them...

Step-by-step explanation:

To find the angle between two vectors, we can use the dot product formula. Given vectors a = a1i + a2j + a3k and b = 4i + 4j + k with an angle of 90 degrees between them, we can equate the dot product to zero:

a · b = |a||b|cosθ

Substituting the values, we have:

a1(4) + a2(4) + a3(1) = 0

Simplifying, we get:

4a1 + 4a2 + a3 = 0

This equation represents a plane in the three-dimensional space, and its normal vector is 4i + 4j + k. Therefore, the vector a is perpendicular to this plane, and any vector perpendicular to this plane is of the form a = t(4i + 4j + k), where t is a scalar.