Question

Q. 3. Find the direction cosines of the line which bisects the angle between positive direction of Y
and Z axes
Q. 4. Find the angle between the lines whose direction ration are 5, 12,- 13 and 3, -4,5
Q. 5. Find the direction cosines of the line which is perpendicular to the lines with direction ratios
-1, 2, 2 and 0, 2, 1

Answer 1

Answer:

Bangkok behind Kahuna's

Answer 2

Question 3:

• The vector parallel to the angle between the positive direction of Y And Z axes = i^+j^

• Unit vector = j/√2 + k/√2

• Therefore the direction cosines are (0,1/√2,1/√2)

Question 4:

• The angle between the lines whose direction ratios are 5,12,13 and 3,-4,5 is

• cos theta= a1 a2+b1 b2+c1 c2/(√a1^2+b1^2+c1^2 √a2^2+b2^2+c2^2)
• cos theta = 15-48-65/(√338+√50)
• cos theta = -0.7538
• theta = 0.999913

Question 5:

The direction cosines of the line perpendicular to the line will be

~a×~b = [i j k

-1 2 2

0 2 1]

= - 2i +j - 2k

Therefore the direction cosines of the required line are = -2 1 -2