Given vectors a = 4i+5j−k, b = i−4j+5k, and c=3i+j−k Find a vector d which is perpendicular to both

In this video, we solve a problem involving vectors to find a vector that is perpendicular to both given vectors 𝑏 and 𝑐, and its dot product with 𝑎 equals 21.

Problem statement : Given vectors a = 4i+5j−k, b = i−4j+5k, and c=3i+j−k. Find a vector d which is perpendicular to both c and b and d⋅a=21

Solution :
Method 1: Let d = x i + y j + z k
d⋅a = 21
d⋅b = 0
d⋅c = 0

Substitute a, b, c, and d into the above equations:

(4x + 5y - z) = 21
(x - 4y + 5z) = 0
(3x + y - z) = 0

Solve for x, y, z to get d

Method 2 :
We start with the given vectors 𝑎, 𝑏, and 𝑐, and use the cross product to find the perpendicular vector 𝑑. Watch the full video to see the step-by-step solution and understand the concepts of vector cross product and dot product calculation.


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Please watch: "Mastering Trigonometry : Comprehensive Guide to Trigonometric Functions and Identities"
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